名校
解题方法
1 . 已知
,
分别为双曲线
:
的上、下两个焦点,点
恰为抛物线
:
的焦点,记点
为两曲线的一个公共点,且
,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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d373d735a7abcadb76e499cbcca51a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c2f156b05838deaae6a35acad242af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/053e4bc2221a29664bff05c3fe0a8075.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
解题方法
2 . 双曲线
的左,右顶点分别为
,右焦点
到渐近线的距离为
为双曲线
在第一象限上的点,则下列结论正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4334568ab6d5d54fb95da96f87da0b51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.双曲线![]() ![]() |
B.双曲线![]() ![]() |
C.设直线![]() ![]() ![]() ![]() ![]() |
D.若直线![]() ![]() ![]() ![]() |
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3 . 设椭圆
与双曲线
(其中
)的离心率分别为
,
,且直线
与双曲线的左、右两支各交于一点,下列结论正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33558881906c228c262ff8024dcfc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33a99190a8fd29c36d5a002e3197cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a560f37921b2fd014c60c4f5b5266d0.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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解题方法
4 . 通过双曲线的学习,我们知道函数的图象是“等轴双曲线”,其离心率为
,经深入研究发现函数
的图象也是双曲线,且直线
和
是它的渐近线,那么
的离心率是
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解题方法
5 . 已知双曲线
的右焦点为F,直线
是C的一条渐近线,P是l上一点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f02ae557a40e8cadc9ab7b8a451d5b6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd52bdd5ffba5f2c465cf42e9f13169.png)
A.C的虚轴长为![]() | B.C的离心率为![]() |
C.![]() | D.直线PF的斜率不等于![]() |
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2024-03-21更新
|
2073次组卷
|
8卷引用:湖北省“荆、荆、襄、宜四地七校”考试联盟2023-2024学年高二下学期期中联考数学试卷变式题6-10
(已下线)湖北省“荆、荆、襄、宜四地七校”考试联盟2023-2024学年高二下学期期中联考数学试卷变式题6-10江苏省南通市2024届高三第二次调研测试数学试题江苏省扬州市2024届高三第二次调研测试数学试题江苏省泰州市2024届高三第二次调研测试数学试题(已下线)第三套 艺体生新高考全真模拟 (二模重组卷)(已下线)第二套 艺体生新高考全真模拟 (二模重组卷)(已下线)江苏省泰州市2024届高三第二次调研测试数学试题变式题6-10(已下线)江苏省南通市2024届高三第二次调研测试数学试题变式题 6-10
名校
6 . 某数学兴趣小组的同学经研究发现,反比例函数
的图象是双曲线,设其焦点为
,若
为其图象上任意一点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f42b2a9736c8943106472a7398d2892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.![]() | B.它的离心率为![]() |
C.点![]() | D.![]() |
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2024-03-14更新
|
1948次组卷
|
8卷引用:湖北省荆州市沙市中学2023-2024学年高二下学期3月月考数学试题
名校
解题方法
7 . 设
是双曲线
的右焦点,
为坐标原点,过
作
的一条渐近线的垂线,垂足为
,若
的内切圆与
轴切于点
,且
,则
的离心率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d028cebfbc0e84421b3fcfd09b1fa26e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f1dda6cc1affb91bb49756fa6a04459.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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2024-03-06更新
|
293次组卷
|
2卷引用:湖北省新高考联考协作体2023-2024学年高二下学期2月收心考试数学试题
8 . 已知双曲线方程为
,
,
为双曲线的左、有焦点,离心率为2,点
为双曲线在第一象限上的一点,且满足
,
.
(1)求双曲线的标准方程;
(2)过点
作斜率不为0的直线
交双曲线于
两点;则在
轴上是否存在定点
使得
为定值,若存在,请求出
的值及此时
面积的最小值,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.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/113db2d0c72e095d1c6194654e3904fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fff6bd26743c0d4c0961b889ff86e7c1.png)
(1)求双曲线的标准方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61608b9b3eee2858eb6cc0f66afa3dd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d871b0b46194d7300950e04f085533d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e8c7968d57d2a20065a7cb15c9b4eb.png)
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2024-02-27更新
|
251次组卷
|
2卷引用:湖北省武汉市新洲区部分学校2023-2024学年度高二上学期期末质量检测数学试卷
解题方法
9 . 已知双曲线
的中心在原点,对称轴为坐标轴,且经过点
,
,则下列结论中错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad20e2bc6576fc461419f8f138d26e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/584e5ab4eda0422eafac89816dde6a55.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.直线![]() ![]() |
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解题方法
10 . 双曲线具有如下光学性质:从一个焦点出发的光线,经双曲线反射后,反射光的反向延长线经过另一个焦点.如图,已知双曲线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c5c2e64358e0ec7aa142c336d970306.png)
为双曲线
的左、右焦点.某光线从
出发照射到双曲线右支的
点,经过双曲线的反射后,反射光线
的反向延长线经过
.双曲线在点
处的切线与
轴交于点
,且反射光线所在直线的斜率为
.则以下说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c5c2e64358e0ec7aa142c336d970306.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fa8dff314800da92c67a8e98418de01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09264bee5e799e2f646bcff2617efc53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d51ff068cd3924e951ff9137840584e7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/20/58a58fdb-16c5-42c9-8237-d33088734a9a.png?resizew=165)
A.点![]() ![]() ![]() |
B.![]() |
C.双曲线![]() |
D.若过点![]() ![]() ![]() ![]() ![]() |
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