1 . 已知双曲线
的左、右焦点分别为
,直线
与
的一条渐近线平行,若点
在
的右支上,点
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14b9a6f6acf5af46a6543c80414abbe3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5640ba51541dce7590c009e5e77a1ff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd371fe0f40dc56b63c92d67c9ffcb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feb1d666dafb5ec27128f2703e51afe5.png)
A.![]() | B.6 | C.![]() | D.8 |
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解题方法
2 . 已知
是等轴双曲线C的方程,P为C上任意一点,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377a2333ff8c63cbdb20b882d6d5a7ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/036818ece5123ca4f8f758ab840e429a.png)
A.C的离心率为![]() |
B.C的焦距为2 |
C.平面上存在两个定点A,B,使得![]() |
D.![]() ![]() |
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2024-04-16更新
|
722次组卷
|
2卷引用:辽宁省名校联盟2024年高考模拟卷(信息卷)数学(五)
名校
3 . 设双曲线
的左焦点和右焦点分别是
,点
是
右支上的一点,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce6a2299a108a5f039461fd8cf8395db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.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/caa8711ff188e86a79f05cf1d90ca05f.png)
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4 . 定长为
的线段AB的端点在双曲线
的右支上运动,则AB中点M的横坐标的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/125b2901f97cc5584137f5d17e546e96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c8e5a57709f0c99507af139b32855da.png)
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5 . 下列结论正确的是( )
A.椭圆![]() |
B.椭圆![]() |
C.双曲线![]() ![]() ![]() ![]() |
D.双曲线![]() ![]() ![]() |
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6 . 已知双曲线
:
的左、右焦点分别为
,
,
是
右支上一点,线段
与
的左支交于点
.若
为正三角形,则
的离心率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.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/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/c5db41a1f31d6baee7c69990811edb9f.png)
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2024-03-03更新
|
993次组卷
|
4卷引用:云南省昆明市第一中学、银川一中2024届高三下学期联合考试一模数学试卷
云南省昆明市第一中学、银川一中2024届高三下学期联合考试一模数学试卷(已下线)专题15 双曲线离心率(一题多解)(已下线)第3讲:圆锥曲线的定义以及应用【讲】云南省开远市第一中学校2023-2024学年高二下学期期中考试数学试题
解题方法
7 . 已知双曲线
的左、右焦点分别为
,
,点
在双曲线
上,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a127e344ccfdaf9cb84ebc7f999080ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
A.![]() |
B.双曲线![]() ![]() |
C.![]() ![]() |
D.![]() ![]() |
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解题方法
8 . 双曲线
:
(
,
)的一条渐近线过点
,
,
是
的左右焦点,且焦点到渐近线的距离为
,若双曲线上一点
满足
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2adb9d51fe350a23e26c9115cc77e0e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b10e8abf8690e4b129466ddb918bcc94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8a952a1380148042d4ef38e491a532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e203545563ef6c33968cd9fab532638e.png)
A.3或7 | B.7 | C.5 | D.3 |
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2024-02-04更新
|
524次组卷
|
3卷引用:四川省成都市树德中学2024届高三上学期期末数学(理)试题
四川省成都市树德中学2024届高三上学期期末数学(理)试题四川省成都市树德中学2024届高三上学期期末数学(文)试题(已下线)3.2.2 双曲线的简单几何性质【第三练】“上好三节课,做好三套题“高中数学素养晋级之路
解题方法
9 . 已知
、
分别是双曲线C:
(
,
)的两个焦点,若双曲线的一条渐近线与直线
恰好平行.
(1)求双曲线C的离心率;
(2)若
,M为双曲线上一点,且
,求
的值﹒
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af449f710cdcbb849672b3dcc2c84bb7.png)
(1)求双曲线C的离心率;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4428ec56246b35cb87bfe7ed50f0ad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a22cc73ff3f197568b1de60f31c0d845.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2675e721a547386255bae4dfdca9ff2.png)
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10 . 设
,
为双曲线
的左右焦点,
为双曲线右支上一点,点
,当
取最小值时,
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a218602e8e3a52f74f760059aa7014.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c10f14aae6fb21e047ecb39cdf40c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f88d872adbdb526b7cf29872b9556532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39387d3ab691f41564b304e66fb51b5f.png)
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