名校
解题方法
1 . 已知双曲线
的左、右焦点分别为
,点P为双曲线E上的一点,且
,射线PN平分
,交x轴于点N,若
,则双曲线E的渐近线方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef66f4832adc43902055a7e6d258037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d124b231bf2cd3746f35e6c68cd7178f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94fe48bf7af022ecbbe13833fdcc2c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ed48037b97600c88f75445c2ea6b412.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
2 . (1)已知双曲线的一条渐近线方程是
,焦距为
,求双曲线的标准方程.
(2)求以双曲线C:
的焦点为顶点,顶点为焦点的椭圆标准方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4541bd6a12515d83b3a2ba8378fed1d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38acfaa0f912c2598cc341ec98da8a08.png)
(2)求以双曲线C:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a0bd4bd9985f1e367c100b453ed03f.png)
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3 . 已知双曲线C:
(
,
),若四个点
,
,
,
(
,
)中有三个点在C上,则该双曲线的渐近线方程为( )
![](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/251102916ec3a64df667c1e14c6dfd89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04529472264cdcd72ac29ead983df370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a55623ea0fe0b6fbd71c3ecc8c04276.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce92b4d36f31085ea8315f249dbf6c53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da663e39e96645a5c44a78501b9d9c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/232d1ce3ad14256b1543e6007ff1675d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
4 . 已知双曲线
与
有相同的渐近线,点
为
的右焦点,
,
为
的左右顶点.
(1)求双曲线
的方程;
(2)过点
倾斜角为
的直线
交双曲线
于
,
两点,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42a960d9c62f797d46caa7a8a4a134a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16717e13ebff71049f609189e8f065c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63309dbc3612815f6dbdee23d9a10adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.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/084cf5ffced059f5653ee2a1023518b7.png)
您最近一年使用:0次
名校
解题方法
5 . 已知双曲线
:
的左、右焦点分别为
,
,
为双曲线
右支上的动点,过
作两渐近线的垂线,垂足分别为
,
.若圆
与双曲线
的渐近线相切,则下列命题正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aea42903faa3269a8296a317d65644d8.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50907d33ee3ebbdcdc3bc0e8aa5d523d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.双曲线![]() ![]() |
B.![]() |
C.![]() |
D.若直线![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2024-02-27更新
|
251次组卷
|
2卷引用:湖南省长沙市第一中学2023-2024学年高二下学期开学自主检测数学试题
名校
解题方法
6 . 已知圆
与中心在原点、焦点在
轴上的双曲线
的一条渐近线相切,则双曲线
的离心率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/949a21d6f1a4bc5a3247bc7e2ddec19b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
您最近一年使用:0次
解题方法
7 . 经过双曲线
的右焦点
作该双曲线的一条渐近线的垂线
,垂足为
,且
交另一条渐近线于点
,若
,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3e6bc84e6adc74f093afc8946146076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf0a855871e1687dac94280df0b822c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
8 . 已知
分别为双曲线
的左、右焦点,过双曲线
右支上一点
作直线
交
轴于点
,交
轴于点
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/007fac72e804a2d3093b372e051eab77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50376118e6e3e9a43b08b194077fc9cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/386f652252ffec6d721ee40c7d781e58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
A.双曲线![]() ![]() |
B.双曲线![]() ![]() |
C.点![]() ![]() |
D.四边形![]() |
您最近一年使用:0次
解题方法
9 . 已知曲线
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea98e440bfde1774250b29a86a215b0d.png)
A.当![]() ![]() |
B.当![]() ![]() ![]() |
C.存在实数![]() ![]() ![]() |
D.当![]() ![]() ![]() |
您最近一年使用:0次
2024-02-24更新
|
297次组卷
|
4卷引用:河南省部分名校2023-2024学年高二上学期1月期末考试数学试题
10 . 已知双曲线
,直线
与C交于A,B两点,点P是C上异于A,B的一点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82c4ed5a210e7f97bf194e37fd38ad8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3016baf1a9ce777f16ea9ce469b2510.png)
A.C的焦点到其渐近线的距离为![]() |
B.直线![]() ![]() |
C.过C的一个焦点作弦长为4的直线只有1条 |
D.点P到两条渐近线的距离之积为![]() |
您最近一年使用:0次