组卷网>高中数学综合库>平面解析几何>圆锥曲线>椭圆>椭圆的离心率>根据离心率求椭圆的标准方程
题型:解答题 难度:0.4 引用次数:303 更新时间:2019/12/20 16:41:59 题号:9171381
已知椭圆CeqId64c86c3bcdf740b78e496c40c4394dbb上的点到右焦点F的最大距离为eqIdcc6cd7cd413040b2a3c3fe1e9db3cc15,离心率为eqId449049f2695f40c98ceea2d52ca646e8
说明: figure
eqId7b0c876472714a72ae295f233fb0622a求椭圆C的方程;
eqId6a74229c63d7479c8ff55ba05baf9afe如图,过点eqId52bbc156c300478a97e2e205a280e7a4的动直线l交椭圆CMN两点,直线l的斜率为eqIdd0574f12db424b6db12e8019bc05d754A为椭圆上的一点,直线OA的斜率为eqId0a36e30a683349969ee31af225fd4aa9,且eqId16d321e277bd4bdeb97153cf5071f920B是线段OA延长线上一点,且eqId52211adb3c7b448d8ff121fe267cabcc过原点O作以B为圆心,以eqIdc2f8c873da284f81badbb2142879b394为半径的圆B的切线,切点为eqIdd11462a2c9a84700a67c3f88728b9311eqId68d80f3b1ca04fd1a52aeb47a01f2e51,求eqIddd718397f23e4ef2a61a1290edad7131取值范围.

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解答题 | 较难(0.4) |
解题方法
【推荐1】已知椭圆eqId211c15b061ee47039dccbca908ea32b4的离心率为eqIdb5d311d26c8e43fea598bc6e245b0397,椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的上顶点到右顶点的距离为eqIda2a0ce3781fa4c26b624f5966b7dee44eqId2efda802d5534f6d92d9f8af7aaec28b为坐标原点.
(1)求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的标准方程;
(2)若eqIdd63bac86f3134a5893cc3557f233e1c4是椭圆eqId19a4eb16029e4550a14f2afe4741a3c3上两点(异于顶点),且eqId3f944f49aea6464cbd4397177ac32fac的面积为eqId5f816d038c584dc7a249120298677ef3,设射线eqId31135bdd9784458eb7fa26812c2b6ab6eqId3421afc5f6cd4acaa73a12be41636df5的斜率分别为eqId67aae67f8f18439e8c51ebb0260bd192,求eqId9468d11c131648c69733d83b72f21675的值;
(3)设直线eqId417e80f1349244878d01fe90e0891f5f与椭圆交于eqId71891062a8724584af9a2c4c77cd566e两点(直线eqId417e80f1349244878d01fe90e0891f5f不过顶点),且以线段eqId996e2048847f41d5a5fe0e2282909254为直径的圆过椭圆的右顶点eqIdcc614bd3390c4d028df189b234dcc351,求证:直线eqId417e80f1349244878d01fe90e0891f5f过定点.
更新:2020/11/06组卷:323
解答题 | 较难(0.4) |
解题方法
【推荐2】在平面直角标系eqId2272a344734c4fb088737b84294f7219中,点eqId6588e97ba4f1490d8bf3a568c5d63f02在椭圆eqIda955c67e2f754a27baf764a3c657eb49上,且椭圆的离心率eqIde4d58f42bad9461b93d451da718fc6f4.
(1)求椭圆M的标准方程;
(2)过椭圆M的右顶点A作椭圆M的两条弦eqId99a3187c2b8f4bcc9703c74c3b72f1f3eqIdcf2da96900c948a1b3ce7cbfd420c080,记直线eqId99a3187c2b8f4bcc9703c74c3b72f1f3eqIdcf2da96900c948a1b3ce7cbfd420c080eqId0627be51821d4be7b3e024a354815d64的斜率分别为eqIdd4bf9298f0db4fb5afb67e0d739f3074eqId75fdb198d83447e59e31c1f4923cc3bceqId4d2187284c5d4de29906363f7d21f60f,其中eqIdd4bf9298f0db4fb5afb67e0d739f3074eqId75fdb198d83447e59e31c1f4923cc3bc的值可以变化,当eqIde052bbcb4ee04c788e97e80679050379,求eqId473dfcabd8e24941afa1af139d175ce2的所有可能的值.
更新:2020/08/06组卷:277
解答题 | 较难(0.4) |
【推荐3】已知椭圆eqId19a4eb16029e4550a14f2afe4741a3c3eqId625d9676fe044829b8fa3047296c3d8feqIda0815893bebd4a9eb9ef5b0bc94a2bcf为焦点,且离心率eqId5dd2923dcdc745f98f1bb0ad5e9e62d1
(1)求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的方程;
(2)过eqId43cf649947194bc4b9a910a5f39819a2点斜率为eqId4d2187284c5d4de29906363f7d21f60f的直线eqId74c7e0292b094e54ae596d37798a05ed与椭圆eqId19a4eb16029e4550a14f2afe4741a3c3有两个不同交点eqIdbedf755e0fdb4d078d6859360706b163eqId75a143b898e14ccdb032561fba9da811,求eqId4d2187284c5d4de29906363f7d21f60f的范围;
(3)设椭圆eqId19a4eb16029e4550a14f2afe4741a3c3eqId8e15963708e9415da25069fea5906e24轴正半轴、eqId072d7d6b911b42bc89207e72515ebf5f轴正半轴的交点分别为eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c,是否存在直线eqId74c7e0292b094e54ae596d37798a05ed,满足(2)中的条件且使得向量eqId8377c315e74d47479c7767db14b71bbfeqId3719fcad464c419291c2d254d26e10f2垂直?如果存在,写出eqId74c7e0292b094e54ae596d37798a05ed的方程;如果不存在,请说明理由.
更新:2018/10/16组卷:1556
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