组卷网>知识点选题>构造齐次方程法求离心率的值或范围
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1 . 已知eqId5f04473e64c141bcbe9b0a8af27f4aa8是椭圆和双曲线的公共焦点,eqIdbedf755e0fdb4d078d6859360706b163是他们的一个公共点,且eqId946c4dba2607485f8b441c97ff031826则椭圆和双曲线的离心率的平方之和的最小值为(   )
A.eqIdebbe713a11804639ba2f0394a9b255e2B.eqId41cd3b6102dc4aacbd01087c95731363C.eqId999ea08a1da146f39bf99bdeba9f3d9fD.eqIdb08ff1ca14c249cdb13cbb657ac45e37
2 . 设椭圆eqId9026e6d24e404bb2808fe83705f83954的左、右焦点分别为eqId5f04473e64c141bcbe9b0a8af27f4aa8A是椭圆上一点,eqId8bdfeebc7bfd43bcbdc57a3d7644d859,若原点eqId2efda802d5534f6d92d9f8af7aaec28b到直线eqId4640d2096f684733917f4179d5c5b9fd的距离为eqId2cb82e5a53914d2ba65b165860bae6a1,则该椭圆的离心率为____
3 . 已知eqId2efda802d5534f6d92d9f8af7aaec28b为坐标原点,双曲线:eqId3327c113c43b4f7191d1fa2c69c46c60eqId982da3835b7946d999cc8604a2ece266eqId8164502d09d44990ac4f2f73ea67e37a)的左焦点为eqId63db14a5b4334f3ea583c8fb12b0d175,左顶点为eqId052844cae8574a8ab842c38a039baac0,过点eqId63db14a5b4334f3ea583c8fb12b0d175向双曲线的一条渐近线作垂线,垂足为eqIdbedf755e0fdb4d078d6859360706b163,且eqIde9566b6900fe4977ab2ba18c9a97d490,则该双曲线的离心率为______
4 . 已知ABP是椭圆eqIdc99abb1d7d224f51aa5e8cf8686f53a4上的三个不同的点.O为坐标点,eqId33ed4937f0414f76bc72387c68d942e8,且eqIde7b64708244e4fb093754125b48b5e94,则椭圆C的离心率为______.
5 . 如图所示,点F是椭圆eqId0fa9a83824094360bbeb51ccc9e745af的右焦点,AC是椭圆上关于原点O对称的两点,直线eqId211ab513a02842808eee31b029297b06与椭圆的另一个交点为B,若eqIdad488dad542f403a9664491af73f8b30,则椭圆M的离心率为(   )
说明: figure
A.eqIdf304702bf4d04282970e845827d5a8f8B.eqId49b7b111d23b44a9990c2312dc3b7ed9C.eqIde4d58f42bad9461b93d451da718fc6f4D.eqId11a75c651d0a45c6a582be841e9561cf
6 . 已知椭圆eqIddea2714cfe984323977f11c744ee6adb短轴上的两个三等分点与两焦点构成一个正方形.
(1)求椭圆的离心率;
(2)若直线eqId417e80f1349244878d01fe90e0891f5f为圆eqId890d748855bb440ab671e9dfe7a66306的一条切线,eqId417e80f1349244878d01fe90e0891f5f与椭圆eqId19a4eb16029e4550a14f2afe4741a3c3交于eqIdeb53cb7cb0274f7d8f111c60f824c243两点,且eqIdb999cf88922246ebae67a8ebb4083277eqId2efda802d5534f6d92d9f8af7aaec28b为坐标原点),求椭圆的方程.
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7 . 已知点eqId63db14a5b4334f3ea583c8fb12b0d175为椭圆eqId76662bc293df4139b90c65ed8b136d3beqId207ddd75d0ee42629ce30bec7dcdaba1)的左焦点,过原点eqId2efda802d5534f6d92d9f8af7aaec28b的直线eqId417e80f1349244878d01fe90e0891f5f交椭圆于eqIdbedf755e0fdb4d078d6859360706b163eqId75a143b898e14ccdb032561fba9da811两点,点eqId2381423d4cd146cab95f55527681a766是椭圆上异于eqIdbedf755e0fdb4d078d6859360706b163eqId75a143b898e14ccdb032561fba9da811的一点,直线eqId931ba899d97a4e2cb3e45188a59009c9eqId10a7e54dcd3f45feb36c6019ba40d64a分别为eqIdd4bf9298f0db4fb5afb67e0d739f3074eqId75fdb198d83447e59e31c1f4923cc3bc,椭圆的离心率为eqIdf035b8f27d4645bb9f6a66f4a3f51918,若eqId5978eadcddb24426b077595c83fd08f7eqIde9cb4ec0409748978978fe52ac8e429f,则(   )
A.eqId41f89345ebdb442fa5ffdba06b891766B.eqId8a52ea9284fe4cb2a25df5dd3da0fb80C.eqId0148dc702ab0462597c27fb2d1586177D.eqIdd903b029cd9c4c95bc7f2e1deb98845a
9 . 已知椭圆eqId211c15b061ee47039dccbca908ea32b4AF分别是椭圆C的左顶点和左焦点,圆eqIda420d870e88b4910aecbf3bfb4856199,过左焦点FeqId3f6e9a9c17094da79cde85a037255767轴,交圆O于点P,直线AP恰好与圆O相切,则椭圆C的离心率为___________.
10 . F1F2是椭圆eqId85f1422d857f4becb684e20a5fc1f913的左、右焦点,过点F2作直线eqId6c505de085b547319fe6395d300febdb 交椭圆于eqId71891062a8724584af9a2c4c77cd566e两点,现将椭圆所在平面沿直线eqId8cc868c8728549b7856b34482929deef折成平面角为锐角eqIdc13953f2514e4c8f9c8aaaf5241c33ac的二面角,翻折后eqId71891062a8724584af9a2c4c77cd566e两点的对应点分别为eqId4e5e54e051f84915979ba70b82179bb5eqIdbdf19ed09bd34fc8af6790b826d13449,且eqId723e69f3d005490eaaa6a66e6fcd6dde
(1)求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的离心率;
(2)设直线eqId5abb35f584304bfe803335a0bb897aa7与椭圆eqId19a4eb16029e4550a14f2afe4741a3c3在第一象限的交点为eqIdbedf755e0fdb4d078d6859360706b163eqId8754ce8cf7f34f04abb9a0c041f57f5c为椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的上顶点,且直线eqId417e80f1349244878d01fe90e0891f5f与直线eqId078a55bed08847b4b2fa537fd90d14d4交于点eqId75a143b898e14ccdb032561fba9da811,若eqId217233d5de78420faa88cd52250b118f,求eqId4d2187284c5d4de29906363f7d21f60f的值.
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