椭圆四：面积问题

椭圆四：面积问题 椭圆四:有关面积问题 1.(2010一模)海淀 19((本小题满分13分) 3 已知椭圆C的中心在原点，焦点在轴上，左右焦点分别为，且，点(1，) xFF,||2FF,12122 在椭圆C上. (?)求椭圆C的方程; 122AB,lC(?)过的直线与椭圆相交于两点，且的面积为，求以为圆心 F,AFBF1227 l且与直线相切的圆的方程. : 19((本小题满分13分) 22xy解:(?)设椭圆的方程为，由题意可得: ，,,,1,(0)ab22ab 椭圆C两焦点坐标分别为，. .……………1分 F(1,0),F(1,0)12 33532222？,，，，,，,，,2(11)()(11)()4a. .……………3分 2222 2c,1b,,,413又 ， ……………4分 ？,a2, 22xy，,1故椭圆的方程为. .……………5分 43 33l,xAB(1,),(1,),,,(?)当直线轴，计算得到:， 22 11SABFF,,,,，，,||||323，不符合题意. .……………6分 ,AFB12222 ll当直线与轴不垂直时，设直线的方程为:， xykx,，(1) ykx,，(1),,222222由，消去y得 ， .……………7分 (34)84120，，，,,kxkxk,xy，,1,43, ,,0AxyBxy(,),(,)显然成立，设， 1122 228412kk,xxxx，,,,,,,则 .……………8分 1212223434，，kk 42644(412)kk,222又||1()41ABkxxxxk,，,，,,,，,, 1212222(34)34，，kkintegrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, 2212112(1)kk，，2即 ， .……………9分 ||1ABk,，,,223434，，kk |10|2||kkk，,，又圆的半径 .……………10分 Fr,,,22211，，kk 221112(1)2||12||1122kkkk，，所以 SABr,,，,,,||,,AFB22222234347，，kk1，k 42化简，得， 17180kk，,, 22k,,1即，解得 (1)(1718)0kk,，, 2||k所以，， .……………12分 r,,221，k 22故圆的方程为:. .……………13分 F(1)2xy,，,2 l(?)另解:设直线的方程为 ， xty,,1 xty,,1,,2222,,0由，消去x得 ，恒成立， (43)690，,,,tyty,xy，,1,43, 69t设，则 ……………8分 yyyy，,,,,,,AxyBxy(,),(,)12121122224343，，tt 22121t，3636t2所以 ,;||()4yyyyyy,,，,,,，121212222243，t(43)43，，tt .……………9分 |101|2,，，t又圆的半径为， .……………10分 Fr,,22211，，tt 21121122t，2t,1所以，解得， SFFyyyy,,,,,,,,||||||,AFB121212222437，t 2所以， ……………12分 r,,221，t 22F故圆的方程为:. .……………13分 (1)2xy,，,2 2.朝阳(2011一模理) 19((本小题满分14分) CCFPABA(2, 0),B(2, 0)已知，为椭圆的左、右顶点，为其右焦点，是椭圆上异于，的动点， ,APB23且面积的最大值为( C(?)求椭圆的方程及离心率; integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, (?)直线与椭圆在点处的切线交于点，当直线绕点转动时，试判断以 APBDAPABD 为直径的圆与直线的位置关系，并加以证明( PF 答案:19((本小题满分14分) 22xyC解:(?)由题意可设椭圆的方程为，( ，,,,1(0)abFc(,0)22ab 1y,,,223,abD,2,Pc,1由题意知解得，( b,3,a,2, E,222,abc,，. OxFBA 22xy1C故椭圆的方程为，离心率为(……6分 ，,1243 (?)以BD为直径的圆与直线PF相切( 证明如下:由题意可设直线AP的方程为. ykx,，(2)(0)k, 则点DBDE坐标为，中点的坐标为( (2, 4)k(2, 2)k ykx,，(2),,,222222由得( (34)1616120，，，,,kxkxk,xy，,1,43, 21612k,P设点的坐标为，则( ,,2x(,)xy000234，k 268,k12kx,所以，ykx,，,(2)( ……………………………10分 0002234，k34，k F因为点坐标为， (1, 0) 13PD(1, ),k,,当时，点的坐标为，点的坐标为. (2, 2),22 22PFx,BDPF直线轴，此时以为直径的圆与直线相切( (2)(1)1xy,，,, 1y4k0PFk,,当时，则直线的斜率. k,,PF22xk,,1140 4kPFyx,,(1)所以直线的方程为( 214,k 328kk，84kk,,2k22214,k1414,,kkEPFd,点到直线的距离( ,,2||k2214，k16k，1222|14|,k(14),k 1dBD,||||4||BDk,又因为 ，所以( 2 integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, 故以为直径的圆与直线相切( BDPF 综上得，当直线绕点转动时，以为直径的圆与直线相切(………14分 APABDPF3.(2011顺义二模理19). (本小题满分14分) 3 已知椭圆C的左，右焦点坐标分别为,离心率是。椭圆C的左，右顶点分，，，，F,3,0,F3,0122 10别记为A,B。点S是椭圆C上位于轴上方的动点，直线AS,BS与直线分别交于M,N两点。 l:x,,x3(1) 求椭圆C的方程; 2) 求线段MN长度的最小值; ( 1,TSA(3) 当线段MN的长度最小时，在椭圆C上的T满足:的面积为。试确定点T的个数。 5 c322解(1)因为，且c,3，所以 ,a,2,b,a,c,1a2 2x2 所以椭圆C的方程为 …………………………………………….3分 ，y,14 kk,0 (2 ) 易知椭圆C的左，右顶点坐标为,直线AS的斜率显然存在，且 A(,2,0),B(2,0) 104M(,,,k) 故可设直线AS的方程为，从而 y,k(x，2)33 y,k(x，2),22222 由得 (1，4k)x，16kx，16k,4,0x,2，y,1,4 2216k,42,8k(,2)x,x, 设，则，得 S(x,y)1111221，4k1，4k 2,kk2844kSy,(,) 从而，即 12221，4k，k，k1414 1y,,(x,2) 又,故直线BS的方程为 B(2,0)4k 110,,y,,(x,2)x,,,,1044k3N(,,) 由得，所以 ,,10433k,,x,,y,,33k,, 4k4MN,， 故 33k 4k44k48k,0MN,，,2,, 又，所以 33k33k3 4k4k,1, 当且仅当时，即时等号成立 33k 8k,1 所以时，线段MN的长度取最小值 ………………………………..9分 3 integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, k,1 (3)由(2)知，当线段MN的长度取最小值时， 64此时AS的方程为，, S(,,)x,y，2,055 421y_ ,TSA 所以,要使的面积为， AS,55 D_ N_ S_ 2 只需点T到直线AS的距离等于， B_ x_ 4O_ A_ M_ 2' 所以点T在平行于AS且与AS距离等于的直线上 l4 t,2352't,或t, 设，则由，解得 ,l:x,y，t,02242 2,x2，y,1,324? 当时，由得 t,5x，12x，5,0,32,x,y，,02, ',,44,0 由于，故直线与椭圆C有两个不同交点 l 2,x2，y,1,524?t,时，由得5x，20x，21,0 ,52,xy,，,02, ',,,20,0由于l，故直线与椭圆C没有交点 综上所求点T的个数是2. … 4.(2010寒假)东城 19((本小题满分13分) C2:1已知椭圆的中心在原点，一个焦点，且长轴长与短轴长的比是( F(0,2) C(?)求椭圆的方程; CPPPAPB1(?)若椭圆在第一象限的一点的横坐标为，过点作倾斜角互补的两条不同的直线，分 CABAB别交椭圆于另外两点，，求证:直线的斜率为定值; ,PAB(?)求面积的最大值( 答案: 19((本小题满分13分) 22yxC，,,,1(0)ab解,,?,设椭圆的方程为, 22ab 222,abc,，, ,,ab:2:1,,由题意 ………………………………………………2分 , ,c,2.,, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, 22解得 ，, a,4b,2 22yxC，,1所以椭圆的方程为,………………………………………………4分 42 k(?)由题意知，两直线，的斜率必存在，设的斜率为， PAPBPB 则的直线方程为. PBykx,,,2(1) y A ,ykx,,,2(1),P F,1 22由得 ,yx，,1.,B ,42x O 222.………………6分(2)2(2)(2)40，，,，,,,kxkkxkF 2 设，，则 Axy(,)Bxy(,)AABB 2kk,,222， xx,,,1BB22，k 2kk，,222同理可得， x,A22，k 8k42k则，. yykxkx,,,,,,,(1)(1)xx,,ABABAB222，k2，k yy,ABAB所以直线的斜率为定值. ……………………………………8分 2k,,ABxx,AB AB(?)设的直线方程为. yxm,，2 ,yxm,，2,,222242240xmxm，，,,由得. ,yx，,1.,,42 222m,8由，得.……………………………………10分 ,,,,,(22)16(4)0mm 2m,42mxx,,此时，. xx，,,ABAB42 mPABd,到的距离为， 3 22ABxxyy,,，,()() ABAB 32,,，m12 2 integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, m1132 则,,,,SABdm12,PAB2223 2211118mm,，22. ,,，,，,mm(8)222222 2因为使判别式大于零， m,4 m,,2所以当且仅当时取等号， 所以面积的最大值为(………………………………………………………13分 ,PAB25. (2010一模)石景山 19((本题满分14分) 22xy6 已知椭圆的离心率为，长轴长为，直线交椭圆于不同23，,1(a,b,0)l:y,kx，m223ab 的两点A、B。 (1)求椭圆的方程; (2)求的值(O点为坐标原点); m,1,且OA,OB,0,求k 3l,AOB (3)若坐标原点O到直线的距离为，求面积的最大值。 2答案: 19((本题满分14分) 解:(1)设椭圆的半焦距为c， ,c6,,, 依题意 a3, ,a,3, c,2 解得 222 由 2分 a,b，c,得b,1. 2x2，y,1. 所求椭圆方程为 3分 ？3 (2)？m,1,？y,kx，1. 设A(x,y),B(x,y)， 1122 2,x2y，,1, 其坐标满足方程 3, ,ykx,，1, y 消去并整理得 22 4分 (1，3k)x，6kx,0, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, 222(*) 5分 则,,,，,,(6)4(13)(33)0kkk 2,,633kk 故 6分 xxxx，,,,,1212221313，，kk ？AO,OB,0 ？，,，，,，xxyyxxkxkx(1)(1)12121212 22 ,，，，，(1)()kxxkxxk1212 223363kkk,,,222 ,，，,，,,(1)0kkk222131331，，，kkk ？,,k3 ？,,k3 经检验满足式(*)式 8分 |m|3 (3)由已知， ,221，k 322m,(k，1) 可得 9分 4 222,kx，m 将代入椭圆方程，整理得 y(1，3k)x，6kmkx，3m,3,0. 222 ,,(6km),4(1，3k)(3m,3),0(*) 2,kmm,633？x，x,x,x,,. 10分121222，k，k1313 2223612(1)kmm,2222 ？,，,,,,||(1)()(1)[]ABkxxk2122(31)31kk，， 2222212(k，1)(3k，1,m)3(k，1)(9k，1) 11分 ,,222(3k，1)(3k，1) 212k1212,3，,3，,3，,4(k,0) 12分 4212，3，69k，6k，129k，，62k 129k, 当且仅当， 2k 3k,, 即时等号成立， 3 3k,, 经检验，满足(*)式 3 integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, k,0时， 当|AB,3 综上可知13分 |AB|,2.max 133,AOB 当|AB最大时，的面积最大值 14分 S,，2，,？222 6.海淀(2011寒假) 19. (本小题满分14分) 2C已知点在抛物线上，点到抛物线的焦点F的距离为2，直线MMy(1,)(0)p,Cypx:2, 1AB,l:与抛物线交于两点. yxb,,，2 C(?)求抛物线的方程; (?)若以为直径的圆与轴相切，求该圆的方程; xAB l,AOB(?)若直线与轴负半轴相交，求面积的最大值. y 答案: 19. (共14分) p2解:(?)抛物线 的准线为， .....................................1分 (0)p,ypx,2x,,2 pp由抛物线定义和已知条件可知， ||1()12MF,,,,，,22 2解得，故所求抛物线方程为. ......................................3分 p,2yx,4 1,yxb,,，,2(?)联立，消并化简整理得. xyyb，,,8802,2,yx,4, ,,，,64320bb,,2依题意应有，解得. ..............................................4分 设，则， .............................................5分 AxyBxy(,),(,)yyyyb，,,,,8,811221212 xxyy，，1212xy,,,,,4设圆心Qxy(,)，则应有. 000022 因为以为直径的圆与轴相切，得到圆半径为， ........................6分 xry,,||4AB0 2222又 . ||()()(14)()5[()4]5(6432)ABxxyyyyyyyyb,,，,,，,,，,,，1212121212 所以 ， .........................................7分 ||25(6432)8ABrb,,，, 8解得. .........................................8分 b,,5 4824所以，所以圆心为. (,4),xxbybyb，,,，,,，,2222416121255 2422故所求圆的方程为. ............................................9分 ()(4)16xy,，，,5 方法二: integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, 1,yxb,,，,22，消掉并化简整理得， 联立xbxb,，，,(416)40y2,2,yx,4, 22依题意应有，解得b,,2. ............................................4分 ,,，,,16(4)160bb 2设，则 . .............................................5分 xxbxxb，,，,416,4AxyBxy(,),(,)11221212 xxyy，，1212设圆心，则应有， xy,,,,,4Qxy(,)000022因为以为直径的圆与轴相切，得到圆半径为. .....................................6分 xry,,||4AB0 152222又 ， ||()()(1)()[()4]5(6432)ABxxyyxxxxxxb,,，,,，,,，,,，121212121244又，所以有， .............................................7分 ||28ABr,,5(6432)8，,b 8解得， ..............................................8分 b,,5 2448所以，所以圆心为. xx，,(,4),1255 2422故所求圆的方程为. .............................................9分 ()(4)16xy,，，,5 lb,0(?)因为直线与轴负半轴相交，所以， y lb,,2,,,20b又与抛物线交于两点，由(?)知，所以，...........................................10分 1lyxb,,，直线:整理得， xyb，,,2202 |2|2,,bbOl点到直线的距离 ， .................................................11分 d,,55 132所以. ..................................................12分 SABdbbbb,,,，,，||422422,AOB2 32,,,20b令，， gbbb()2,， 42， ,gbbbbb()343(),，,，3 444 b,(2,),,(,0), 333 ,gb() ， , 0 gb() 极大 432gb()由上表可得最大值为 . ...............................................13分 g(),,327 3234,AOB所以当时，的面积取得最大值 . ...............................................14分 b,,93 7.东城(2011一模理) (19) (本小题共13分) 22yx2，,,,1(0)ab已知椭圆的离心率为，且两个焦点和短轴的一个端点是一个等腰三角形22ab2 integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, l的顶点(斜率为的直线过椭圆的上焦点且与椭圆相交于，两点，线段的垂直平分线与Pkk(0),QPQ 轴相交于点( yMm(0,) (?)求椭圆的方程; (?)求的取值范围; MPQ(?)试用表示?的面积，并求面积的最大值( 答案:(19)(共13分) c2b,c解:(?)依题意可得，，， ,a2 222又， a,b，c 可得( ba,,1,2 2y2所以椭圆方程为( ，,x12 l (?)设直线的方程为， ykx,，1 ykx,，1,,,222由可得( (2)210kxkx，，,,,y2，,x1,,,2 设， PxyQxy(,),(,)1122 ,2k1xx，,则xx,,，( 121222k，2k，2 4yykxx，,，，,()2可得( 12122k，2 ,k2NN(,)设线段中点为，则点的坐标为， PQ22kk，，22 由题意有k,k,,1， MN 2m,2k，2可得,,,k1( k 2k，2 1m,可得， 2k，2 k,0又， 10,,m所以( 2 F(?)设椭圆上焦点为， integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, 1则. SFMxx,,,,,MPQ122 28(1)k，2， xxxxxx,,，,,()412121222(2)k， 112由，可得( m,k，,22k，2m 18(1),mxxmm,,,,8(1)所以( 121 2m 又， FMm,,1 3Smm,,2(1)所以. ,MPQ 132m(1,m)0,m,所以?的面积为()( MPQ2 3设， f(m),m(1,m) 2则( f'(m),(1,m)(1,4m) 111(0,)(,)可知在区间单调递增，在区间单调递减( f(m)424 1271f(),(0,)所以，当时，有最大值( f(m)4644 136(0,)所以，当时，?的面积有最大值( MPQ48 8.(2011西城二模理19.)(本小题满分14分) 22xy22M:1，,已知椭圆的离心率为，且椭圆上一点与椭圆的两个焦点构成的三角(0)ab,,22ab3 6，42形周长为( M?)求椭圆(的方程; lCMAB(?)设直线与椭圆交于两点，且以为直径的圆过椭圆的右顶点， AB, ,ABC求面积的最大值( M6，42解:(?)因为椭圆上一点和它的两个焦点构成的三角形周长为， 2a，2c,6，42所以， ……………1分 22c2222ca,又椭圆的离心率为，即，所以， ………………2分 ,33a3 a,3c,22所以，. ………………4分 integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, 2x2所以，椭圆的方程为. ………………5分 M，y,1b,19 1BCAC(?)方法一:不妨设的方程，则的方程为. y,,(x,3)ynxn,,,(3),(0)n ynx,,(3),,1,22222由得， ………………6分 (，n)x,6nx，9n,1,0,x29，,y1,9, 设，， A(x,y)B(x,y)1122 2227n,3819n,因为，所以x,， ………………7分 3x,22229n，191n， 227,3n同理可得， ………………8分 x,129，n 221，n6n62|BC|,1，n所以，|AC|,， ………………10分 229n，1n9，n 12(n)，1nS|BC||AC|,,， ………………12分 ,ABC16422(n)，，n9 1t,n，,2设， n 223t则， ………………13分 S,,,646428tt，，99t 8t,当且仅当时取等号， 3 3,ABC所以面积的最大值为. ………………14分 8 AB方法二:不妨设直线的方程. xkym,， xkym,，,,,2222由 消去得， ………………6分 x(9)290kykmym，，，,,,x2，,y1,,9, 设A(x,y)，B(x,y)， 1122 2m,92kmyy，,,yy,则有，. ? ………………7分 121222k，9k，9 ,,,,,,,, CABCACB,,0因为以为直径的圆过点，所以 . ,,,,,,,, CAxyCBxy,,,,(3,),(3,)由 ， 1122 (3)(3)0xxyy,,，,得 . ………………8分 1212 integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, 代入上式， 将xkymxkym,，,，,1122 22得 . (1)(3)()(3)0kyykmyym，，,，，,,1212 12m,3将 ? 代入上式，解得 或(舍). ………………10分 m,5 1212所以(此时直线经过定点，与椭圆有两个交点)， m,D(,0)AB55 1所以 SDCyy,,||||,ABC122 213925(9)144k，,2. ……………12分 ,，，,,()4yyyy12122225525(9)k， 11设， tt,,,,02k，99 91442Stt,,,，则. ,ABC525 2513所以当时，取得最大值. t,,(0,]S,ABC82889 9.(2010寒假)崇文 (19)(本小题共14分) O已知椭圆的中心在坐标原点，焦点在轴上，短轴长为2，且两个焦点和短轴的两个端点恰为一个x lFP正方形的顶点(过右焦点与轴不垂直的直线交椭圆于，两点( xQ(?)求椭圆的方程; l(?)当直线的斜率为1时，求的面积; ,POQ OF(?)在线段上是否存在点,使得以为邻边的平行四边形是菱形, Mm(,0)MPMQ, 若存在，求出的取值范围;若不存在，请说明理由. m y P F O Mx Q 答案: 19)(共14分) 22xy，,,,10ab解:(?)由已知，椭圆方程可设为( ----------------1分 ，，22ab ? 两个焦点和短轴的两个端点恰为正方形的顶点，且短轴长为2， ? ( bca,,,1,2 integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, 2x2( ---------------- 4分 所求椭圆方程为，,y12 l(?)右焦点，直线的方程为( F1,0yx,,1，， 设， PxyQxy,,,，，，，1122 22,xy，,22,12由 得 ，解得 ( yy,,,1,3210yy，,,,123yx,,1,, 112? ( ----------------9分 SOFyyyy,,,,,,,POQ1212223 OF(?)假设在线段上存在点,使得以为邻边的平行四边形是菱形(因为Mmm,001,,MPMQ,，，，， l直线与轴不垂直，所以设直线的方程为( ykxk,,,10x，，，， 22,xy，,22,,2222由 可得( 124220，,，,,kxkxk，，,ykx,,1,，，,, 22422kk,?( xxxx，,,,1212221212，，kk uuuruuuruuur MPxmyMQxmyPQxxyy,,,,,,,,,,,, (其中 xx,,0，，，，，，1122212121 为邻边的平行四边形是菱形 以MPMQ, uuuruuuruuuruuuruuuruuur,，,,，,,MPMQPQMPMQPQ0 ，，，， ,，,，,,,xxmyyxxyy2,,0 ，，，，12122121 ,，,,，，,,(2)()()()0xxmxxyyyy12211221 ,，,，，,(2)()0xxmkyy 1212 2244kk2,,，,,(2)(2)0mk 221212，，kk 2k22,,,mk0,,，,2240kkm( ，，，，212，k 10,,m?( ----------------1 4分 2 10.丰台18.(本小题满分13分) 22OlPQ、已知为平面直角坐标系的原点，过点的直线与圆xy，,1交于两点( M(2,0), ,,,,,,,,1lOPOQ,,,(?)若，求直线的方程; 2 ,OMPl(?)若,OPQ与的面积相等，求直线的斜率( l解:(?)依题意，直线的斜率存在， llM(2,0),ykx,，(2)因为 直线过点，可设直线:( integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, ,,,,,,,,22因为 两点在圆上，所以 ， OPOQ,,1PQ、xy，,1 ,,,,,,,,,,,,,,,,,,,,,,,,11因为 ，所以 OPOQ,,,OPOQOPOQPOQ,,,,，,,cos22 1:O所以 l 所以 到直线的距离等于( ，,POQ1202|2|1k所以 ， ,22k，1 15 得， k,,15 l所以 直线的方程为或…………………6分 xy,，,1520xy，，,1520 ,,,,,,,,,,OMP(?)因为与的面积相等，所以， ,OPQMQMP,2 ,,,,,,,,, 设 ，，所以 ，( Pxy(,)Qxy(,)MQxy,，(2,)MPxy,，(2,)11222211xx，,，22(2)xx,，2(1),,2121所以 即 (*); ,,yy,2yy,221,,21 P因为 ，两点在圆上， Q 2222,,xy，,1xy，,1,,1111所以 把(*)代入，得 ， ,,2222xy，,14(1)41xy，，,,,,2211, 7,x,,，1,8,所以 ,15,y,,(1,8, 1515l所以 直线的斜率kk,,,， 即………………………13分 k,,MP99 integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed,