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 . 已知点eqId5f04473e64c141bcbe9b0a8af27f4aa8分别是双曲线eqId3327c113c43b4f7191d1fa2c69c46c60的左右焦点,过eqId0aa72756ed0c4c7a89f26aa94f43e47d且垂直于eqIda9cd3f94eb8045438f75e9daccfa7200轴的直线与双曲线交于eqIdeb53cb7cb0274f7d8f111c60f824c243两点,若eqId9ac8f5dbc275451280c88a998a64aa89为等边三角形,则该双曲线的离心率eqIdf035b8f27d4645bb9f6a66f4a3f51918是(   )
A.eqIda2a0ce3781fa4c26b624f5966b7dee44B.eqIda2a0ce3781fa4c26b624f5966b7dee44eqIda0a63338a10c422289029e7524739222C.2D.3
2 . 已知eqId0aa72756ed0c4c7a89f26aa94f43e47d是双曲线eqId3327c113c43b4f7191d1fa2c69c46c60eqId982da3835b7946d999cc8604a2ece266eqIdd123017a4fc941db9c1d31ba22efcefd)的左焦点,点eqIdbedf755e0fdb4d078d6859360706b163在双曲线上,直线eqId837ff378f14241e39d932f0cc9ac064deqIda9cd3f94eb8045438f75e9daccfa7200轴垂直,且eqId12041b0c425541d7b9368089431156dc,那么双曲线的离心率是(   )
A.eqId3385c7d74629435abd34488e4cc89b4cB.eqIda2a0ce3781fa4c26b624f5966b7dee44C.2D.3
3 . 双曲线eqIda6d3d00ca52748cd8370b775f1762b6d的左焦点为eqId63db14a5b4334f3ea583c8fb12b0d175,过eqId63db14a5b4334f3ea583c8fb12b0d175eqIda9cd3f94eb8045438f75e9daccfa7200轴垂线交eqId93cbffaa5ae045d6ac45d1e979991c3a于点eqId052844cae8574a8ab842c38a039baac0,过eqId63db14a5b4334f3ea583c8fb12b0d175作与eqId93cbffaa5ae045d6ac45d1e979991c3a的一条渐近线平行的直线交eqId93cbffaa5ae045d6ac45d1e979991c3a于点eqId8754ce8cf7f34f04abb9a0c041f57f5c,且eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5ceqIda9cd3f94eb8045438f75e9daccfa7200轴同侧,若eqId9f2a9556034e46d0b69e65dacf4e7840,则eqId93cbffaa5ae045d6ac45d1e979991c3a的离心率为_______
4 . 已知双曲线eqId58ecc109d7934cbb921c58754c302a4b的左、右焦点为eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e,在双曲线上存在点eqIdbedf755e0fdb4d078d6859360706b163满足eqIdb08bb8527eef4842a14c76b8cc48adef,则此双曲线的离心率eqIdf035b8f27d4645bb9f6a66f4a3f51918的取值范围是(   )
A.eqId49eb45c36a6a4ca5a9d4deb01bc99fffB.eqId79e523e0e415404d91aa887cfd5b2ff1C.eqId24fdcbb736074ddbaa7bdd942923ae1fD.eqId69787711fae2410c976ce4dd5a44ad79
多选题 | 一般(0.65) | 2022·全国高三专题练习
5 . 已知双曲线eqId0dfb68cc9cd9497a95e5763983333886,右顶点为A,以A为圆心,b为半径作圆A,圆A与双曲线C的一条渐近线交于MN两点,若eqId4fdc7d076cf1413c94bb8533a5bbf1fa,则有(   )
A.渐近线方程为eqId1baf8570a3074034ba800379e1ae30a1B.eqId2cb7e2c624e74cbb97dafa014ce32525
C.eqId0ac91d6fd7dd41d8aca80d0a0a60972aD.渐近线方程为eqId4114d054e35047019c8724c257b68f5b
更新:2021/09/14组卷:0
6 . 已知双曲线eqIdceed1a7797e443d9abdce2f0c8179d8e的左、右焦点分别为eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e,点eqId052844cae8574a8ab842c38a039baac0是双曲线在第一象限的点,若eqIdc85a253fbb3e4b75b9bae91dc7e88f94eqId54ef3a72198a4b24a738a7364cf825cb,则双曲线eqId19a4eb16029e4550a14f2afe4741a3c3的离心率eqId798d7463abda4e278ad50ee077068a1d(   )
A.eqId3385c7d74629435abd34488e4cc89b4cB.eqIda2a0ce3781fa4c26b624f5966b7dee44C.eqId47eb7f5d137e421597f229247be6a46dD.eqId15755fd7039d4760803209c0bada9344
7 . 以双曲线eqIdceed1a7797e443d9abdce2f0c8179d8e的右焦点eqId3d9114a85cdc4b06bccb4bfd48b17415为圆心,eqId70a27b6ddf6b478285353abb3b1f3741为半径的圆与eqId19a4eb16029e4550a14f2afe4741a3c3的一条渐近线交于eqIdeb53cb7cb0274f7d8f111c60f824c243两点,若eqIddecb5ba5e6f847b397b2e5c90211bc1d,则双曲线eqId19a4eb16029e4550a14f2afe4741a3c3的离心率为_________
8 . 已知双曲线eqId3327c113c43b4f7191d1fa2c69c46c60a>0,b>0)的左、右焦点分别为F1F2.过点F2且斜率为eqIdc01ce533903e40babea15183683f0bf4的直线与双曲线在第一象限的交点为M.若eqId400df18c60f941f7a60e9b6b79bee000,则此双曲线的离心率为___________.
9 . 已知eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e分别为双曲线eqId19a4eb16029e4550a14f2afe4741a3c3eqId58ecc109d7934cbb921c58754c302a4b的左、右焦点,P是其右支上一点,若eqId0627b001fb8f4ab39064a023ba39cc3deqId00cb39930e1a413789dc52c7ff917028eqId361eb569741e434887f08e95fc82e738成等差数列,且eqId5d59bd69cd384274be893f9818109ba6是直角三角形,则双曲线的离心率是___________.
10 . 已知eqIdde963a24921f4ee7a991bf9d4f43a42e是双曲线eqId19a4eb16029e4550a14f2afe4741a3c3eqId6d3651a43ff940ba8b6641aa75577d68的右焦点,则eqIdde963a24921f4ee7a991bf9d4f43a42e到双曲线eqId19a4eb16029e4550a14f2afe4741a3c3的渐近线的距离为__________;过点eqIdde963a24921f4ee7a991bf9d4f43a42e,斜率为eqIde6ea793b6b434e32a8ab09f8697c35e1的直线交双曲线的右支于AeqId8754ce8cf7f34f04abb9a0c041f57f5c两点(其中点AeqIda9cd3f94eb8045438f75e9daccfa7200轴上方),且满足eqIdbc6e7deb50874c2a8387fd1975cde7b2,则双曲线的离心率为___________.