2024高三·全国·专题练习
1 . 若动点
满足方程
,则动点P的轨迹方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44ee82573986d4fa6a7ee1b5f397edae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e1b62c6b5cc93866ecec180f0b971e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024·全国·模拟预测
名校
2 . 已知
分别为双曲线
的左、右焦点,点
是
上一点,点
满足
,
,则
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22767745d20f5f525a8545ea81942fc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b81ff4917bdee5b26f15ce5373e77727.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024·全国·模拟预测
解题方法
3 . 已知双曲线
的左焦点为
,过
的直线
与圆
相切,切点为
,
交双曲线
的右支于点
,且
,则
的离心率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e4be819fc47b2aa19ab2022b3dfeb6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24de9612f96309c86cac955fa2522e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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解题方法
4 . 已知双曲线
上一点到两个焦点的距离之差的绝对值为8,虚轴长为6,则
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.2 | D.![]() |
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解题方法
5 . 已知
为双曲线
的两个焦点,
为
上一点,若
,且
为等腰三角形,则
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4434ddd2d694b30c9425140a3a238392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.2 | C.![]() ![]() | D.2或3 |
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2024-04-15更新
|
851次组卷
|
5卷引用:专题4 离心率题 定义方程 【练】
(已下线)专题4 离心率题 定义方程 【练】(已下线)2024年高考全国甲卷数学(文)真题平行卷(提升)(已下线)2024年高考全国甲卷数学(理)真题平行卷(提升)陕西省榆林市2023-2024学年高三第二次模拟检测数学(理科)试题陕西省榆林市2024届高三第二次模拟考试文科数学试题
解题方法
6 . 已知双曲线
的左、右焦点分别为
,过原点
的直线
与
交于
两点.若
,且
的面积为2,则
的焦距为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1d92dd0a05d851324698a0f543b03e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca8b6ac96dfe0046b7ca1745176ca22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f557f299ed5bf2d6c65ba308bbfff6d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd78bac276e6c7b0a47e0b9743402a4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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解题方法
7 . 已知
分别是双曲线
的左、右焦点,
为双曲线上两点,满足
,且
,则双曲线
的离心率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098a3e7d1f1890863b7483a98b618119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b21a71ea5ac95da62c80eaf502ed922.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4921e3e11e5596e4686a7d293859294.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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解题方法
8 . 已知圆M:
的圆心为M,圆N:
的圆心为N,一动圆与圆N内切,与圆M外切,动圆的圆心E的轨迹为曲线C.
(1)证明:曲线C为双曲线的一支;
(2)已知点
,不经过点
的直线
与曲线C交于A,B两点,且
.直线
是否过定点?若过定点,求出定点坐标:若不过定点,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adae65d2fe79e2cad4a89baa0a7d19d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef42b93cd533d22b80e54593a249f008.png)
(1)证明:曲线C为双曲线的一支;
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d56ab70e602f2e2e291df643ab209162.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b768ea6a05cbf45b28fc46c501ba532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2024-04-13更新
|
808次组卷
|
3卷引用:模块7专题6 正交于顶 模型优先练
2024高三·全国·专题练习
9 . 已知双曲线
的左、右焦点分别为
,过
作倾斜角为
的直线交双曲线
的右支于点
,交
轴于点
,
的内切圆与
相切于点
,若
,
,则双曲线
的焦距为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3b52af1d93cf91437881f823ad19623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/183b6a0cef4256c9696a5bca31053da5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19176bc9ba1c6efb999a349c31580a95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce54a6a6fae9f2c26537e4334059ea8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
10 . 设
是双曲线
的左、右焦点,点A是双曲线C右支上一点,若
的内切圆M的半径为a(M为圆心),且
,使得
,则双曲线C的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40f98254a6193566587a70c7d95fdabf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c29bab2a74ca02d30e0deed068b042f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2cfd997d3b66a3b8f7731b26f0ab0c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06f1aa3b0edcdba0073e2b8f1b141817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7853aa81790c329227d3c9cc4beb1bd8.png)
A.![]() | B.![]() | C.2 | D.![]() |
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2024-04-10更新
|
2136次组卷
|
6卷引用:数学(新高考卷03,新题型结构)
(已下线)数学(新高考卷03,新题型结构)(已下线)第1题 双曲线的离心率问题(5月)(压轴小题)(已下线)【讲】 专题三 平面向量与其他知识的交汇问题(压轴大全)辽宁省大连市2024届高三下学期第一次模拟考试数学试卷山西省部分学校2023-2024学年高二下学期5月质量检测数学试题山西省吕梁市2023-2024学年高二下学期5月质量检测数学试卷