解题方法
1 . 已知双曲线
:
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e66fbc91467ed4996d82707a6120b1fb.png)
A.双曲线![]() | B.双曲线C的焦点在y轴上 |
C.双曲线![]() ![]() | D.双曲线C的离心率![]() |
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解题方法
2 . 已知双曲线
左、右焦点分别为
、
,
、
为双曲线一条渐近线上的两点,
为双曲线的右顶点,若四边形
为矩形,且
,则双曲线
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c91e2ddf362dc348b6603abde27a6f84.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c482f270b5d1961f03d5a58c9912867c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56ad1164f00c6c8ed67468c023541535.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-01-25更新
|
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|
2卷引用:江苏省无锡市第一中学2023-2024学年高二上学期期末考试数学试题
2024·全国·模拟预测
解题方法
3 . 已知过点
可作出双曲线
的两条切线,切点都在双曲线
的同一支上,则双曲线
的离心率的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497911bc462170183e81d95bd509b70b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
4 . 已和双曲线
与直线
相交于A、B两点,若弦
的中点M的横坐标为1,则双曲线C的渐近线方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa6342e0a5a8942cfb1cf535ceb2c50d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-01-22更新
|
448次组卷
|
3卷引用:重庆市第十八中学2023-2024 学年高二上学期期末考试数学试题
重庆市第十八中学2023-2024 学年高二上学期期末考试数学试题(已下线)【类题归纳】弦的中点 可深可浅(课本典例)山东省潍坊市第一中学2023-2024学年高一下学期清明后摸底考试(4月月考)数学试题
5 . 已知双曲线C:
的一个焦点为
则该双曲线的渐近线方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8deb4fc9c16ea91b834d08433779716c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3409f30cef3f6e4ef85debb85d7c16b.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024-01-21更新
|
89次组卷
|
2卷引用:内蒙古自治区赤峰市红山区2023-2024学年高二上学期期末学情监测数学试卷(A)
名校
解题方法
6 . 设
,
分别是双曲线
(
,
)的左右焦点,
为双曲线左支上一点,且满足
,直线
与双曲线的一条渐近线垂直,则双曲线的离心率为( )
![](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/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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff00fc29b9b9374935cf7bd256fb6234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
A.![]() | B.![]() | C.2 | D.![]() |
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2024-01-19更新
|
1282次组卷
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3卷引用:天津市四校2023-2024学年高二上学期期末联考数学试卷
解题方法
7 . 已知双曲线
的右焦点为点
,过点
作双曲线
的其中一条渐近线
的垂线,垂足为点
(点
在第一象限),直线
与双曲线
交于点
,若点
为线段
的中点,且
,则双曲线
的方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a477603f3f88c3b48352b6130f9ad5.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a986b6799310790a4fcfab8da6a1ec88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 点
到双曲线
的一条渐近线的距离为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb0e705301752424a492f6277ed7774e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7267e8ea86e072c58eec7c30309820d9.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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9 . 已知双曲线
的右焦点为
,过
作双曲线
的其中一条渐近线
的垂线,垂足为
(第一象限),并与双曲线
交于点
,若
,则
的斜率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/27c068128e953da51ea67a24945ffee3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
10 . 双曲线
的左,右焦点分别为
,O为坐标原点,过
作C的一条渐近线的垂线,垂足为D,且
,则C的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3c8091d78595c42d437ff5766431a8d.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/be9474fb1f2bb58355f7522cf72804d2.png)
A.![]() | B.2 | C.![]() | D.3 |
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