组卷网>高中数学综合库>平面解析几何>圆锥曲线>椭圆>椭圆的标准方程>根据a、b、c求椭圆标准方程
题型:解答题 难度:0.4 引用次数:1001 更新时间:2020/12/3 8:13:09 题号:11910535
已知椭圆eqId0bfe30d7e7ac477f871558e7fad634ab的左、右焦点分别是eqId5f04473e64c141bcbe9b0a8af27f4aa8,且离心率为eqId5f816d038c584dc7a249120298677ef3,点eqId2381423d4cd146cab95f55527681a766为椭圆下上动点,eqId9c85ce533b3f4c73a1913f2b3c5d58e1面积的最大值为eqId37705e1ef6a84bbdbe88433e75932cdf
(1)求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的标准方程;
(2)若eqId2381423d4cd146cab95f55527681a766是椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的上顶点,直线eqId17ab120dd1484145a133e6a409c8465c交椭圆eqId19a4eb16029e4550a14f2afe4741a3c3于点eqId517584fed25c413ba8b7bb33ffa2d5c6,过点eqId0aa72756ed0c4c7a89f26aa94f43e47d的直线eqId417e80f1349244878d01fe90e0891f5f(直线eqId417e80f1349244878d01fe90e0891f5f的斜率不为1)与椭圆eqId19a4eb16029e4550a14f2afe4741a3c3交于eqIdad5a3fe6c747453488b22964c985d62c两点,点eqIdbedf755e0fdb4d078d6859360706b163在点eqId75a143b898e14ccdb032561fba9da811的上方.若eqIde7274e4dd55d46a2bac601b297a1ffd6,求直线eqId417e80f1349244878d01fe90e0891f5f的方程.

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解答题 | 较难(0.4) |
【推荐1】已知椭圆eqId211c15b061ee47039dccbca908ea32b4的上顶点为M、右顶点为N.eqId9d077b0e8046474baac2bfb36c94af2b(点O为坐标原点)的面积为1,直线eqIdf4cf79cbbea14d298940773ea43ed467被椭圆C所截得的线段长度为eqId55a5d70ff2fd49ceab8e7f2ed0ebf7e1.
(1)椭圆C的标准方程;
(2)试判断椭圆C内是否存在圆eqId0cea7eabcaa64ce8ac8918df2ba39c4f,使得圆O的任意一条切线与椭圆C交于AB两点时,满足eqIdc1023dce1ac14cdeb622efee964a4f64为定值?若存在,求出圆O的方程;若不存在,请说明理由.
更新:2021/07/23组卷:199
解答题 | 较难(0.4) |
解题方法
【推荐2】已知椭圆C的中心在原点O,焦点在x轴上,椭圆的两焦点与椭圆短轴的一个端点构成等边三角形,右焦点到右顶点的距离为1.
(1)求椭圆C的标准方程;
(2)是否存在与椭圆C交于AB两点的直线leqId70a7dc7ddbcb4ae5b6d62f8f9e0b111b,使得eqIdf052a254d6474a85b91b356ccf69a236成立?若存在,求出实数m的取值范围;若不存在,请说明理由.
更新:2020/02/13组卷:180
解答题 | 较难(0.4) |
解题方法
【推荐3】已知椭圆eqId76662bc293df4139b90c65ed8b136d3beqId207ddd75d0ee42629ce30bec7dcdaba1)的右焦点为eqIdba800e03c70e4b36ad99f5d841729878,左右顶点分别为eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId4b1ae677328f42e6bd20d4af5ef911c8,过点eqId63db14a5b4334f3ea583c8fb12b0d175的直线eqId417e80f1349244878d01fe90e0891f5f(不与eqIda9cd3f94eb8045438f75e9daccfa7200轴重合)交椭圆eqId19a4eb16029e4550a14f2afe4741a3c3eqId2381423d4cd146cab95f55527681a766eqId517584fed25c413ba8b7bb33ffa2d5c6点,直线eqIdaae32e4842fa46129dbcdfa6f070ce26eqIda9cd3f94eb8045438f75e9daccfa7200轴的交点为eqId0cd8063abf2b458f80091bc51b75a904,与直线eqIdb63ccadd9d1348f7a45824d5e1c38891的交点为eqIdbedf755e0fdb4d078d6859360706b163.
说明: figure
(1)求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的方程;
(2)若eqId95fcd515764b414f87c24f2d1e697956eqId75e22dcfb4154b9fbf1098a8d22aee87,求出点eqIdbedf755e0fdb4d078d6859360706b163的坐标;
(3)求证:eqId052844cae8574a8ab842c38a039baac0eqId517584fed25c413ba8b7bb33ffa2d5c6eqIdbedf755e0fdb4d078d6859360706b163三点共线.
更新:2020/06/25组卷:268
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