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已知椭圆eqId44eec5d313e14529946ed1149c870cff过点eqId46357520a54c40a1905f3dbfc40aa32a,且其中一个焦点的坐标为eqId840202f353d74e6aa6ed712bbd2003a9
(1)求椭圆eqId93cbffaa5ae045d6ac45d1e979991c3a的方程;
(2)若直线eqIdeef438a877c44692912987ff77af8b53与椭圆交于两点eqId3804465f6d584f2f9bd4e1ad9a3dc087,在eqId8e15963708e9415da25069fea5906e24轴上是否存在点eqId2381423d4cd146cab95f55527681a766,使得eqIde2c785a486224acd8476dfb279c81dfa为定值?若存在,求出点eqId2381423d4cd146cab95f55527681a766的坐标;若不存在,请说明理由.
更新:2020/04/04 难度:0.65 题型:解答题 组卷:513
如图,直线eqIdcae57d0c6c30486ea5bfdef5135c731d与椭圆eqId15bfbddeee0143e08c809ecf76ffb129交于eqId8bb868704ca84429be4745c5bb899ffb两点,eqIdcc614bd3390c4d028df189b234dcc351是椭圆右顶点,已知直线eqId99a3187c2b8f4bcc9703c74c3b72f1f3的斜率为eqIda8012d5322b240128851ebf3cd086e12eqId992fe44057cf4492895193f3f5398449的外接圆半径为eqId91f49a316d3f4a459b0af3a7e2686685.
figure
(1)求椭圆的方程;
(2)若椭圆上有两点eqId19f97bded86b49138f9cccc65ed75269,使eqId4b7fa62691334c408fd8f4d92dbfdbfe的平分线垂直eqId5d10544ec73c43e681a785968815d588,且eqId62b7e11ae5f24cbab585a99f450b5251,求直线eqId66d409c343f04cfda647f9bfc7da6b2a的方程.
更新:2020/04/03 难度:0.65 题型:解答题 组卷:0
已知椭圆CeqIdd448b721bc2f41f8bed63e9521739ce3(a>b>0)的左.右顶点分别为AB,离心率为eqId7c83ccf5b4e742538f181cb75d127445,点PeqId33e512517c164e65b1f204f8d19b9ec6为椭圆上一点.
figure
(1) 求椭圆C的标准方程;
(2) 如图,过点C(0,1)且斜率大于1的直线l与椭圆交于MN两点,记直线AM的斜率为k1,直线BN的斜率为k2,若k1=2k2,求直线l斜率的值.
更新:2020/04/03 难度:0.4 题型:解答题 组卷:131
已知椭圆eqId19a4eb16029e4550a14f2afe4741a3c3eqIdd448b721bc2f41f8bed63e9521739ce3eqIde9c1eda3dc0c4304868ea148d833743f)过点eqId6497187c3e4849709685607d2ed2e3dfeqId0b7b5c85fe6842ac90b9a9cef9060c1c.
(1)求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的方程;
(2)设过椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的右焦点eqId63db14a5b4334f3ea583c8fb12b0d175,且倾斜角为eqIdd01b7918993a412cb774dea127f210b6的直线eqId417e80f1349244878d01fe90e0891f5f和椭圆eqId19a4eb16029e4550a14f2afe4741a3c3交于eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,对于椭圆eqId19a4eb16029e4550a14f2afe4741a3c3上任一点eqId2381423d4cd146cab95f55527681a766,若eqId5e3c7b8e915645629827e2470351854d,求eqId58b5f0c58bab4a02b29e37776ead36c5的最大值.
更新:2020/04/02 难度:0.65 题型:解答题 组卷:0
已知椭圆eqIdf4900dc7d6564cc8a98b4bcd45e859d1的左、右焦点分别为eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e,且eqId3adcc214663c4a86b6ab656b138a4aa5,椭圆经过点eqId3c278f82713d44c3bb0fa99bc8767147.
(1)求椭圆的方程;
(2)直线eqId417e80f1349244878d01fe90e0891f5f过椭圆右顶点eqId8754ce8cf7f34f04abb9a0c041f57f5c,交椭圆于另一点eqIdcc614bd3390c4d028df189b234dcc351,点eqId92869ac114124367b45f631d030ed6bd在直线eqId417e80f1349244878d01fe90e0891f5f上,且eqId845eb653a1194819bccd37ca13bd5690.若eqIdbfbb4478746f4aababf33f5ad503799e,求直线eqId417e80f1349244878d01fe90e0891f5f的斜率.
更新:2020/04/02 难度:0.65 题型:解答题 组卷:0
已知椭圆C的中心在坐标原点,经过两点eqId7063803412cd4003948673a35fd10874eqId8d51fc7f5d7c48ef81e4079aec125737.
(1)求椭圆的方程;
(2)过点eqIdc3514b1568dd4007bc934ec628149532的直线l与椭圆交于AB两点,满足eqId76b0bd626d4646989c688c60a0345440,求直线l的方程.
更新:2020/04/01 难度:0.4 题型:解答题 组卷:0
如图,eqIdf63bd695cded4f1aad8f6594e65cc44e分别为椭圆eqIdcb94200200f74d65ac6c5aa8bd8a33d7的左、右焦点,O为坐标原点,eqId7caa9e2475c9497db31ce98838e7c333.椭圆E经过点eqIdaa3a18c0c895482eaf4782b23482ac60.
figure
(1)求椭圆E的方程;
(2)若BC是椭圆E上两个动点,直线eqId99a3187c2b8f4bcc9703c74c3b72f1f3的斜率与直线eqIdcf2da96900c948a1b3ce7cbfd420c080的斜率互为相反数,证明:直线eqId0627be51821d4be7b3e024a354815d64的斜率为定值,并求出这个定值.
更新:2020/04/01 难度:0.4 题型:解答题 组卷:0
已知eqId2efda802d5534f6d92d9f8af7aaec28b为坐标原点,椭圆eqId19a4eb16029e4550a14f2afe4741a3c3eqIdf18b5700afd748c9af08fbce0977010b的两个焦点分别为eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e.点eqIdcf971280f0734ddd9adab874da615a53在椭圆eqId19a4eb16029e4550a14f2afe4741a3c3上,且eqIdbedf755e0fdb4d078d6859360706b163eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e的距离之和为4.
(1)求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的方程.
(2)若过点eqId0e9dc3def63b4ba180a4bcf22f26fa4e的直线eqId417e80f1349244878d01fe90e0891f5f与椭圆eqId19a4eb16029e4550a14f2afe4741a3c3交于eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,以eqId99a3187c2b8f4bcc9703c74c3b72f1f3为直径的圆过eqId2efda802d5534f6d92d9f8af7aaec28b,求直线eqId417e80f1349244878d01fe90e0891f5f的方程.
更新:2020/04/01 难度:0.65 题型:解答题 组卷:0
已知椭圆eqIdebaf59b50bc94fdbaadc6374d8483fda的左焦点为eqIde37106e810ae484a9fdc1366da623244且经过点eqId9a6be60cd3b54977bc21830f4e5eeb55分别是eqId92869ac114124367b45f631d030ed6bd的右顶点和上顶点,过原点eqId2efda802d5534f6d92d9f8af7aaec28b的直线eqId417e80f1349244878d01fe90e0891f5feqId92869ac114124367b45f631d030ed6bd交于eqIdfcf606636c8549158e75f6db78c50096两点(点eqId75a143b898e14ccdb032561fba9da811在第一象限),且与线段eqId99a3187c2b8f4bcc9703c74c3b72f1f3交于点eqId2381423d4cd146cab95f55527681a766.
(1)求椭圆eqId92869ac114124367b45f631d030ed6bd的标准方程;
(2)若eqId4ffb1d8c76b042ef961301aa4f90fed4,求直线eqId417e80f1349244878d01fe90e0891f5f的方程;
(3)若eqIdb159a7d71976407282f0e11176517b1e的面积是eqIdb111cca4394e478199ecec617699aa53的面积的eqIdddd35c5d043e4ebeac32a99367053c68倍,求直线eqId417e80f1349244878d01fe90e0891f5f的方程.
更新:2020/04/01 难度:0.65 题型:解答题 组卷:0