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 . 过双曲线eqIdceed1a7797e443d9abdce2f0c8179d8e的右焦点作直线eqId417e80f1349244878d01fe90e0891f5f,使eqId417e80f1349244878d01fe90e0891f5f垂直于x轴且交CMN两点,双曲线C虚轴的一个端点为A,若eqId63cdf4f3341b4d1aa8afd3a5f8b1d185是锐角三角形,则双曲线C的离心率的取值范围___________
单选题 | 较易(0.85) | 2021·浙江高二期末
3 . 若双曲线eqIdceed1a7797e443d9abdce2f0c8179d8e上存在四个点ABCD满足四边形eqId5ce7a06ae7a34393b92b5277978ac014是正方形,则双曲线C的离心率的取值范围是(   )
A.eqId62107f5c61184320a915c544bc95fdf6B.eqIdf6839377b3804ae1ad1da894ffb4cd38C.eqId82b464f4dc4945f29ef2074304dbaa96D.eqId1c68f3c7891c4d13a8e8d2d37b867461
更新:2021/06/14组卷:0
4 . 已知双曲线CeqId77acaac0f0c14be183c8ee33c6bf6da0=1(a>0,b>0)的左焦点为F,过FC的一条渐近线的垂线l,垂足为AlC的另一条渐近线的交点为B,若A是线段FB的中点,则双曲线C的离心率为__
5 . 过双曲线eqId58ecc109d7934cbb921c58754c302a4b上的任意一点eqIdbedf755e0fdb4d078d6859360706b163,作双曲线渐近线的平行线,分别交渐近线于点eqId2381423d4cd146cab95f55527681a766eqId517584fed25c413ba8b7bb33ffa2d5c6,若eqIdf9cf87f32fb84bfb9f1382c7414b58a8,则双曲线离心率的取值范围是(   )
说明: figure
A.eqIdbdabddb7f5c146a3985db9177a0dafc7B.eqId3590ba3f59d14d529bdf5224a400a064C.eqId5488e9c29a284ce6aff9cb6a460fd426D.eqIdefaecd447bfa4ad9a8b67943a7e83f50
6 . 如图,eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e分别是双曲线eqId3327c113c43b4f7191d1fa2c69c46c60eqId982da3835b7946d999cc8604a2ece266eqId8164502d09d44990ac4f2f73ea67e37a)的左、右焦点,过eqId0aa72756ed0c4c7a89f26aa94f43e47d的直线eqId417e80f1349244878d01fe90e0891f5f与双曲线分别交于eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,若eqId598c8b8c6ad740ba97a4d452e78ddb33,且eqIda8f435b6432649adb7d4b84567dbe3d6,则双曲线的离心率为(   )
说明: figure
A.eqId15d2088f003c4aad9745c07a7616191bB.4C.eqId9a19f81624ec431494b1feeb88f12bdfD.eqIda2a0ce3781fa4c26b624f5966b7dee44
7 . 已知双曲线eqId19a4eb16029e4550a14f2afe4741a3c3eqId0f14428848fa4e8cbdaccdcb9711090d的一个焦点为eqId63db14a5b4334f3ea583c8fb12b0d175,过eqId63db14a5b4334f3ea583c8fb12b0d175作双曲线eqId19a4eb16029e4550a14f2afe4741a3c3的一条渐近线的垂线,垂足为eqId052844cae8574a8ab842c38a039baac0.若eqId8407a8753e404f7e886aa320f2d639f0(eqId2efda802d5534f6d92d9f8af7aaec28b为坐标原点)的面积等于eqId9313a6e74a4a443da4611d2ff7c7a118(eqId44925af6fb19413689ba5616e3647cba为双曲线eqId19a4eb16029e4550a14f2afe4741a3c3的半焦距),则双曲线eqId19a4eb16029e4550a14f2afe4741a3c3的离心率为(   )
A.eqId317ed84d205b4156847380f7e9f38b08B.eqIda2a0ce3781fa4c26b624f5966b7dee44C.2D.eqIdcd9b24a6a6e5426ab775be20461174e3
8 . 已知双曲线eqIda6d3d00ca52748cd8370b775f1762b6d右顶点为eqId052844cae8574a8ab842c38a039baac0,抛物线eqIdd43cdd75670749eda191d9494312c542的焦点为eqId63db14a5b4334f3ea583c8fb12b0d175.若在双曲线的渐近线上存在一点eqIdbedf755e0fdb4d078d6859360706b163,使得eqId12ec9e76d4894f5a8a1ef3eb81384f1c,则双曲线eqId93cbffaa5ae045d6ac45d1e979991c3a的离心率的取值范围是___________.
单选题 | 一般(0.65) | 2021·全国高三其他模拟
9 . 已知双曲线eqIdca9bbb19cd4b49ae8f45dbf75ce5374c的左、右焦点分别为eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42eeqIdbedf755e0fdb4d078d6859360706b163是双曲线右支上一点,eqId2cc8ba14c6414abb87b5721861164d59,直线eqIdf95334ee237f468eb6f7b97d394bd72deqId072d7d6b911b42bc89207e72515ebf5f轴于点eqId75a143b898e14ccdb032561fba9da811,且eqId6fef1001cd684a40b9f5ad8d3e7d0241,则双曲线eqId19a4eb16029e4550a14f2afe4741a3c3的离心率为(   ).
A.eqIda2a0ce3781fa4c26b624f5966b7dee44B.3C.eqIdcd9b24a6a6e5426ab775be20461174e3D.eqId23eb097be91249a0a4f124dcb91a9585
更新:2021/06/08组卷:0
填空题 | 一般(0.65) | 2021·全国高三其他模拟
10 . 从双曲线的一个焦点发出的光线,经过双曲线反射后,反射光线是散开的,它们就好像是从另一个焦点射出的一样,如图.我国首先研制成功的“双曲线新闻灯”就是利用了双曲线的这个光学性质,已知某“双曲线新闻灯”的轴截面是双曲线的一部分,其中eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e分别为该双曲线的左、右焦点,从eqIdde963a24921f4ee7a991bf9d4f43a42e发出的两条光线(共线反向)分别经过双曲线右支上的点eqId2381423d4cd146cab95f55527681a766和点eqId517584fed25c413ba8b7bb33ffa2d5c6,且经过点eqId2381423d4cd146cab95f55527681a766的光线反射后经过点eqId0cd8063abf2b458f80091bc51b75a904eqIda5df9c434fb94f62adfc6ca9418e7d2f,若点eqId0aa72756ed0c4c7a89f26aa94f43e47d在以点eqId517584fed25c413ba8b7bb33ffa2d5c6为圆心、eqId876037be016c4316885be871978f005b为半径的圆上,则该双曲线的离心率为______
说明: figure
更新:2021/06/08组卷:0
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