名校
解题方法
1 . (1)若方程
所表示的曲线为椭圆,求
的取值范围;
(2)求焦点在
轴上,焦距为
,实轴长和虚轴长相等的双曲线的标准方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/994d9dfe278335fb3176478cc335599b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)求焦点在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b10e8abf8690e4b129466ddb918bcc94.png)
您最近一年使用:0次
2023-10-15更新
|
596次组卷
|
4卷引用:重庆市部分学校2023-2024学年高二上学期第一次月考数学试题
名校
2 . 设为实数,已知双曲线
与椭圆
有相同的焦点
.
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若点
![](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/c2427943a38dcd93c9ec9b735ffc9fe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002ed1ebb2cb936e10ab478789f91c7c.png)
您最近一年使用:0次
2023-10-12更新
|
1448次组卷
|
4卷引用:重庆市育才中学、西南大学附中、万州中学2023~2024学年高二上学期12月联考数学试题
重庆市育才中学、西南大学附中、万州中学2023~2024学年高二上学期12月联考数学试题江苏省徐州市邳州市2023-2024学年高二上学期10月阶段性质量检测数学试题(已下线)专题23 双曲线的几何性质7种常见考法归类 - 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教B版2019选择性必修第一册)(已下线)专题12 双曲线的几何性质8种常见考法归类(2)
名校
解题方法
3 . 已知双曲线
,焦点为
,其中一条渐近线的倾斜角为
,点
在双曲线上,且
.
(1)求双曲线
的标准方程;
(2)若直线
交
于
两点,若
的面积为
,求正实数
的值.
![](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/8ac09dc1ca2cdd7aef28c218763d3e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c1d65ece55d4367f789bd24a865b25.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d00a5df9d281dd4e1e45bf6a4d6fb27.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/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-06-09更新
|
1115次组卷
|
3卷引用:重庆市第一中学2022-2023学年高二下学期期中数学试题
名校
解题方法
4 . 已知离心率为
的双曲线C与椭圆
的焦点相同.
(1)求双曲线C的标准方程;
(2)求双曲线C的焦点到渐近线的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d59ab85c075a09d55d69e159e4abb268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0232be17d441190a227f0204ea0ca98.png)
(1)求双曲线C的标准方程;
(2)求双曲线C的焦点到渐近线的距离.
您最近一年使用:0次
2023-09-19更新
|
909次组卷
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7卷引用:重庆市云阳县云阳高级中学校2023-2024学年高二上学期第二次月考数学试题
名校
5 . 已知双曲线
的离心率为
,实轴长为
.
(1)写出双曲线的渐近线方程;
(2)直线
与双曲线右支交于不同的两点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ffe6000b292a0ce7d93601d946e44c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
(1)写出双曲线的渐近线方程;
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd55f837e9c4e6bba1163ef13edd09b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2023-02-07更新
|
1092次组卷
|
6卷引用:重庆市永川北山中学校2022-2023学年高二下学期入学考试数学试题
解题方法
6 . 设双曲线
,点
,
是双曲线
的左右顶点,点
在双曲线
上.
(1)若
,点
,求双曲线
的方程;
(2)当
异于点
,
时,直线
与
的斜率之积为2,求双曲线
的渐近线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.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)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/198fe541f7adf150d03ffb7fe3da8df0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6a15f2579aa50941300a9dd57f56dc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800c5e266b4ad8462a46970f0a232d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46b053f98b1d05a2043e94eeaefea87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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7 . 已知双曲线
的左、右焦点分别为
为双曲线
上一点,
,且焦点到渐近线的距离为
.
(1)求双曲线
的方程;
(2)设
为双曲线
的左顶点,点
为
轴上一动点,过
的直线
与双曲线
的右支交于
两点,直线
分别交直线
于
两点,若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76ed463bf16c78a4bbb9d3acff922afa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50c62b25d9a9fc8496a0e8890c1c76eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](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/76338d35a153967d7a061b4cd9c85183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d42cb68c5c877a455ba7ac0a6b6a651.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede97915bccd6a7b22d7400c30f8adea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fe7fd9b0c3c203a053a7ea52b71e7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcc0e2d4e554dd176b061a4134d2c41b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2022-12-19更新
|
346次组卷
|
2卷引用:重庆市好教育联盟2022-2023学年高二上学期12月调研数学试题
名校
8 . 双曲线
,右焦点为
.
(1)若双曲线
为等轴双曲线,且过点
,求双曲线
的方程;
(2)经过原点
倾斜角为
的直线
与双曲线
的右支交于点
是以线段
为底边的等腰三角形,求双曲线
的离心率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ddd191da6ce40a21e1714fb63afe61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a249981677be834a50f9d28c0c1803e6.png)
(1)若双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88b082e1ddfbf8a6f8b91d137e548827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
(2)经过原点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701f3b0e2bedfe5195443459072d798e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87bdc81d39b4e94273334bef1cd56b24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a159de0b2d9eb1ae0b7e664e64d3c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b652271ab8703724cf54f9b9c110e52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cad4595d5352b2884568a59d8d766a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
您最近一年使用:0次
2022-10-18更新
|
1170次组卷
|
5卷引用:重庆市第一中学校2022-2023学年高二上学期10月月考数学试题
9 . 已知在平面直角坐标系
中的双曲线
,它的中心在原点,焦点在
轴上,
,
分别为左、右焦点,
,离心率为5.
(1)求双曲线
的标准方程;
(2)在双曲线右支上一点
满足
,试判定
的形状.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/8725396e8316c31c876f9fd08e05083f.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)在双曲线右支上一点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35589481c700a3f8fc9ae02c02a1e56d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
您最近一年使用:0次
名校
解题方法
10 . 已知双曲线
的方程为
,直线
.
(1)求双曲线
的渐近线方程、离心率;
(2)若直线
与双曲线
仅有一个公共点,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a218602e8e3a52f74f760059aa7014.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffecff6a416ff88fa84767c40919f1b8.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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