组卷网>知识点选题>直接法解决离心率问题
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1 . 已知双曲线eqId3327c113c43b4f7191d1fa2c69c46c60eqId982da3835b7946d999cc8604a2ece266eqId8164502d09d44990ac4f2f73ea67e37a)与直线eqIded6cd434bbc54f549219629a15aa7be6相交于eqId2381423d4cd146cab95f55527681a766eqId517584fed25c413ba8b7bb33ffa2d5c6两点,直线eqId417e80f1349244878d01fe90e0891f5f上存在一点eqIdbedf755e0fdb4d078d6859360706b163满足eqId946e1b175e6a411ba81fa5b71c90f75c,坐标原点为eqId2efda802d5534f6d92d9f8af7aaec28b,直线eqIda668e52822264c18a05bbdd44d38eb84的斜率为2,则该双曲线的离心率为(   )
A.eqIda2a0ce3781fa4c26b624f5966b7dee44B.eqIdb2392e11e33f4b2fa394e10c28280d94C.eqId317ed84d205b4156847380f7e9f38b08D.3
2 . 已知点eqIdbedf755e0fdb4d078d6859360706b163是双曲线eqIdf8fa5fb016434b1bb372ab39635f8d89右支上一点,eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e分别是eqId19a4eb16029e4550a14f2afe4741a3c3的左、右焦点,eqId2efda802d5534f6d92d9f8af7aaec28b是坐标原点,eqId77d089adc3b34215b55aafe092e7207a,则(   )
A.双曲线eqId19a4eb16029e4550a14f2afe4741a3c3离心率为eqId737d7241bd534a9b8645a03265240eb4
B.双曲线eqId19a4eb16029e4550a14f2afe4741a3c3的渐近线方程为eqIdc0b6f6ff6f9c4fb785473ff0c3095d9a
C.eqId840af3124e08473c8660c6ecf81c75ce
D.△eqIda92d58b10653408fa6707249995ea6d2的面积为eqIdc6a764b97a734b47a9ce62f36819c417
3 . 双曲线eqId19a4eb16029e4550a14f2afe4741a3c3eqId58ecc109d7934cbb921c58754c302a4b的右焦点为eqIdde963a24921f4ee7a991bf9d4f43a42e,过点eqIdde963a24921f4ee7a991bf9d4f43a42e且倾斜角为eqId236bfe74f1024849b3818a5cd741f299的直线与双曲线右支交于eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,则双曲线离心率的取值范围为(   )
A.eqIda8cefae4538f4c9b904b4491ca9f377dB.eqId9d4b7394307a4157bfb96e0524148832
C.eqId521457dd3b824811ac49f07ef9e7a442D.eqIdcb79cfbd0e8a43b49fc80ab6ff77de1c
4 . 双曲线eqIdca9bbb19cd4b49ae8f45dbf75ce5374c的左、右焦点分别为eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42eeqIdbedf755e0fdb4d078d6859360706b163是双曲线eqId19a4eb16029e4550a14f2afe4741a3c3上一点,eqId5771ca52f0234a9eb80e8039954ed6a5轴,eqId3aeb65e1c3fe43acbcdcd5751306a0a0,则双曲线的离心率为(   )
A.eqId8e3ab4836a874ab593bb67a2bce00575B.eqId317ed84d205b4156847380f7e9f38b08C.eqIda2a0ce3781fa4c26b624f5966b7dee44D.eqIdc052ddfbd4524f67a79e0e77c2e5656a
5 . 已知eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e分别为双曲线eqId9f062c0f054448929432dce9c36c22aeeqIdcf49d00b81c64348a4556afc9cc1545f的两个焦点,双曲线上的点eqId43a0b450f6f34f9d8a0a93cdef3f23dc到原点的距离为eqIdaea992e70d4943e49e893817eb885ed7,且eqId4de2cfe24b3946ff955932c8c084993e,则该双曲线的离心率为(   )
A.eqId317ed84d205b4156847380f7e9f38b08B.eqIda2a0ce3781fa4c26b624f5966b7dee44C.2D.3
填空题 | 一般(0.65) | 2021·全国高二课时练习
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6 . 已知eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e是双曲线eqId3327c113c43b4f7191d1fa2c69c46c60(eqId982da3835b7946d999cc8604a2ece266eqId8164502d09d44990ac4f2f73ea67e37a)的左、右焦点,过eqIdde963a24921f4ee7a991bf9d4f43a42e作双曲线一条渐近线的垂线,垂足为点eqId052844cae8574a8ab842c38a039baac0,交另一条渐近线于点eqId8754ce8cf7f34f04abb9a0c041f57f5c,且eqId7b77a32af52b469aad145c50e8fc13d3,则该双曲线的离心率为_______.
更新:2021/07/31组卷:0
7 . 已知是eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e双曲线eqId19a4eb16029e4550a14f2afe4741a3c3eqId3327c113c43b4f7191d1fa2c69c46c60eqId982da3835b7946d999cc8604a2ece266eqId8164502d09d44990ac4f2f73ea67e37a)的左、右焦点,eqIdbedf755e0fdb4d078d6859360706b163是右支上一点,且eqId91b5afff2e5c47d29221db654954eb15eqIdd1e923ddbc36458a84cf2626a7609bcc的直角三角形,则双曲线eqId19a4eb16029e4550a14f2afe4741a3c3的离心率为(   )
A.eqIda2a0ce3781fa4c26b624f5966b7dee44B.eqIda2a0ce3781fa4c26b624f5966b7dee44eqId15755fd7039d4760803209c0bada9344
C.eqId3e1543ad0883432cb23af678b3feacf4D.eqId3e1543ad0883432cb23af678b3feacf4eqId15755fd7039d4760803209c0bada9344
8 . 已知eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e为双曲线eqId074d659016bd4431ac2a50108050acb3的焦点,eqIdbedf755e0fdb4d078d6859360706b163eqIda9eceddfafcd43259b4cdc7d2acd2e7b与双曲线eqIdcfc8599bedfb4ab4944abf141f348a9a的交点,且有eqId5adda57739514e9082941acd6695de0f,则该双曲线的离心率为(   ).
A.eqIdae24098b279f40e9bf0cfc126622203eB.eqIda7a4bdfa79c743ccabecd9fa0d32f42fC.eqId317ed84d205b4156847380f7e9f38b08D.eqIda2a0ce3781fa4c26b624f5966b7dee44
多选题 | 一般(0.65) | 2021·福建高三二模
9 . 设eqId2efda802d5534f6d92d9f8af7aaec28b为坐标原点,eqId5f04473e64c141bcbe9b0a8af27f4aa8是双曲线eqId0f14428848fa4e8cbdaccdcb9711090d的左、右焦点.在双曲线的右支上存在点eqIdbedf755e0fdb4d078d6859360706b163满足eqId733528fbd53f475caaaed68c1320998e,且线段eqId837ff378f14241e39d932f0cc9ac064d的中点eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId072d7d6b911b42bc89207e72515ebf5f轴上,则(   )
A.双曲线的离心率为eqIda2a0ce3781fa4c26b624f5966b7dee44B.双曲线的方程可以是eqId8b1771c99b314c1ea3315da49c9ac557
C.eqIdf0db4cedf67d4eb8a24d432faad58bc7D.eqId4cd2c77f45b74c709061330d26be4e39的面积为eqId9b2303e8b8a6445db22c84131e8cfb69
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