组卷网>知识点选题>利用自变量范围求离心率范围
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| 共计 18 道试题
填空题 | 一般(0.65) | 2021·全国高二课时练习
1 . 如图,以eqId99a3187c2b8f4bcc9703c74c3b72f1f3为直径的圆有一内接梯形eqId5ce7a06ae7a34393b92b5277978ac014,且eqId588db7aaf8e34ddc82aa8ca1e4b643c7.若双曲线eqIdcfc8599bedfb4ab4944abf141f348a9aeqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c为焦点,且过eqId19a4eb16029e4550a14f2afe4741a3c3eqId312ef2c826304089b9b0f1d1e88b0f50两点,则当梯形的周长最大时,双曲线eqIdcfc8599bedfb4ab4944abf141f348a9a的离心率为______
说明: figure
单选题 | 一般(0.65) | 2021·浙江高三开学考试
2 . 已知双曲线CeqId3327c113c43b4f7191d1fa2c69c46c60eqId982da3835b7946d999cc8604a2ece266eqIdd123017a4fc941db9c1d31ba22efcefd)的两条渐近线为eqId74c7e0292b094e54ae596d37798a05edeqId439fb93f7745417b8bb1747d963c6e60,若双曲线C的右支上存在一点P,使得点PeqId74c7e0292b094e54ae596d37798a05edeqId439fb93f7745417b8bb1747d963c6e60的距离之和为b,则双曲线C离心率的取值范围是(   )
A.eqId529f459f3bf547dc8e90c2f4b851ea79B.eqId931cfc27c23f4d03b5f14970b507b2ffC.eqIde30513b0757e4010958954d4b8d6e9e5D.eqId2dbc28f1ee944d9f80138d16f175ae25
3 . 已知双曲线eqId58ecc109d7934cbb921c58754c302a4b右支上存在点P使得P到左焦点的距离等于P到右准线的距离的6倍,则双曲线的离心率的取值范围是____________.
4 . 已知双曲线eqIdca9bbb19cd4b49ae8f45dbf75ce5374c的右顶点为eqId052844cae8574a8ab842c38a039baac0,且以eqId052844cae8574a8ab842c38a039baac0为圆心,双曲线虚轴长为直径的圆与双曲线的一条渐近线相交于eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId19a4eb16029e4550a14f2afe4741a3c3两点,若eqId980fce5bdaa148b0b0181cdcfe573f09,则双曲线eqId19a4eb16029e4550a14f2afe4741a3c3的离心率的取值范围是______________.
多选题 | 一般(0.65) | 2021·江苏南京一中
5 . 已知eqId2efda802d5534f6d92d9f8af7aaec28b为坐标原点,eqId5f04473e64c141bcbe9b0a8af27f4aa8分别为双曲线eqIde720a9cbb0a44a759fedef431a4f6be8的左、右焦点,点eqIdbedf755e0fdb4d078d6859360706b163在双曲线右支上,则下列结论正确的有(   )
A.若eqId48dbb238d67f4a7585bdeddd63d67f04,则双曲线的离心率eqId79e523e0e415404d91aa887cfd5b2ff1
B.若eqId6d3230d868344fc88d6d2808bd9166d8是面积为eqIda2a0ce3781fa4c26b624f5966b7dee44的正三角形,则eqId114187bfa9cc424ab5a01347878fdb0f
C.若eqId894f8d53415741dea8f7a841c68384d1为双曲线的右顶点,eqId5771ca52f0234a9eb80e8039954ed6a5轴,则eqId7c77575cd11b427e81bfda66407327c2
D.若射线eqId80e28c87b2ed44bd9cbb13a0744dc75e与双曲线的一条渐近线交于点eqId75a143b898e14ccdb032561fba9da811,则eqId173f6b053f7949cea65acf16797a5da5
填空题 | 一般(0.65) | 2021·全国
6 . 过双曲线eqIdceed1a7797e443d9abdce2f0c8179d8e的右焦点F引一条渐近线的垂线,垂足为点A、在第二象限交另一条渐近线于点B,且eqId891138a4813244d786faad3b348e6e4f,则双曲线的离心率的取值范围是___________
7 . 已知双曲线eqIdceed1a7797e443d9abdce2f0c8179d8e的左右焦点分别为eqId5f04473e64c141bcbe9b0a8af27f4aa8eqId2efda802d5534f6d92d9f8af7aaec28b为坐标原点,点eqId2381423d4cd146cab95f55527681a766为双曲线右支上一点,若eqIda740853965a34c439089e8f9f7c6b71deqId1b57dc5197214707a095e71fd7c660c4,则双曲线eqId19a4eb16029e4550a14f2afe4741a3c3的离心率的取值范围为(   )
A.eqIdebc6e652adbe46f68526c5a3b85a8d5aB.eqIdac18af787e194f62a386b95d45c3ec62C.eqId872873b4f0e54dfc92d29588f366583cD.eqId963962360ad848539b182adfd563ce24
8 . 设eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e分别为椭圆eqIdcfc8599bedfb4ab4944abf141f348a9aeqIdd448b721bc2f41f8bed63e9521739ce3(eqId207ddd75d0ee42629ce30bec7dcdaba1)与双曲线eqId3a63d00111554b9e8b896929779a293deqId9a92e5a89169441eaf50de6d29b3c09e(eqIdf4bc70e7d42a4148806d5c4dd06c0c12)的公共焦点,设椭圆eqIdcfc8599bedfb4ab4944abf141f348a9a与双曲线eqId3a63d00111554b9e8b896929779a293d在第一象限内交于点eqId2381423d4cd146cab95f55527681a766,且eqId22370f1f76b04ba0ad9fe20fada9d1eb,若椭圆eqIdcfc8599bedfb4ab4944abf141f348a9a的离心率eqIda2d6bc5229684e55babdc5b4c9bc2b49,则双曲线eqId3a63d00111554b9e8b896929779a293d的离心率eqId995e0865ec2840f1a51e3635ece970d5的最小值是________
单选题 | 一般(0.65) | 2021·全国高三专题练习(理)
9 . 已知双曲线eqId0f14428848fa4e8cbdaccdcb9711090d的左、右焦点分别为F1F2,点P在双曲线的右支上,且|PF1|=2|PF2|,则此双曲线的离心率e的范围为(   )
A.(1,+∞)B.(1,3]C.(2,3]D.(1,2]
10 . 已知曲线eqId9226a625513641a59cd2f2d323b43705(   )
A.若eqId7b7abedf6ddf4c4f97e6f16eb709306e,则eqId19a4eb16029e4550a14f2afe4741a3c3为椭圆
B.若eqIdfd24b2152eb0437ebeee67e52b357654,则eqId19a4eb16029e4550a14f2afe4741a3c3为双曲线
C.若eqId19a4eb16029e4550a14f2afe4741a3c3为椭圆,则其长轴长一定大于eqIdc052ddfbd4524f67a79e0e77c2e5656a
D.若eqId19a4eb16029e4550a14f2afe4741a3c3为焦点在eqIda9cd3f94eb8045438f75e9daccfa7200轴上的双曲线,则其离心率小于eqId317ed84d205b4156847380f7e9f38b08
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