解题方法
1 . 已知双曲线的右焦点为
,实轴长为
.
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383f12cb70ca55eba4ff012771dbfa9d.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/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2023-12-27更新
|
702次组卷
|
4卷引用:贵州省遵义市2024届高三上学期12月月考数学试题
解题方法
2 . 已知双曲线
:
的左、右顶点分别为
,
,且顶点到渐近线的距离为
,点
是双曲线
右支上一动点(不与
重合),且满足
,
的斜率之积为
.
(1)求双曲线
的方程.
(2)过点
的直线
与双曲线
交于
轴上方的
,
两点,若
是线段
的中点,
是线段
上一点,且
,
为坐标原点,试判断直线
,
的斜率之积是否为定值.若为定值,求出该定值;若不是,请说明理由.
![](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/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.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/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/b8860d9787671b53b1ab68b3d526f5ca.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23728b4c0467a27d90f71b424f6a946.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/81dea63b8ce3e51adf66cf7b9982a248.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a05793d7de026a194dac40a666e53d2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cad4595d5352b2884568a59d8d766a4.png)
您最近一年使用:0次
2023-06-20更新
|
369次组卷
|
4卷引用:贵州省遵义市2022-2023学年高二下学期期中考试数学试题
3 . 已知
为双曲线
左右焦点,
,且该双曲线一条渐近线的斜率为
,点M和N是双曲线上关于x轴对称的两个点,
为双曲线左右顶点.
(1)求该双曲线的标准方程;
(2)设
和
交点为P,则
的面积是否存在最大值?若存在,请求出这个最大值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c5c2e64358e0ec7aa142c336d970306.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49bcba03fa0b41ed120058ba9eaed0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
(1)求该双曲线的标准方程;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/443a82723ae5cf11aa917362e7db003f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448eb7d301baa90fe59b05761830f81f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
您最近一年使用:0次
2022-05-06更新
|
634次组卷
|
2卷引用:贵州省遵义市2022届高三第三次统一考试数学(理)试题
名校
4 . 已知抛物线
的焦点为双曲线
的一个焦点,那么双曲线的渐近线方程是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4856428c4f87eada4e504fce8cc91d1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0454a4e1f14d5e42c197d8c6d3313377.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2019-04-20更新
|
676次组卷
|
2卷引用:【校级联考】贵州省遵义市2018-2019学年高二下学期五校期中联考数学(文)试题
名校
5 . 双曲线的一个顶点为
,一条渐近线方程为
,则该双曲线的方程是( )
![](https://img.xkw.com/dksih/QBM/2016/6/21/1572762882621440/1572762888232960/STEM/5f96b385a2c840f091d88cd77ae655ab.png)
![](https://img.xkw.com/dksih/QBM/2016/6/21/1572762882621440/1572762888232960/STEM/070d40e5215a463aa6f6d38b77656068.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2016-12-04更新
|
205次组卷
|
2卷引用:2015-2016学年贵州遵义航天高中高二下期中文科数学试卷
13-14高二上·甘肃兰州·期末
6 . 如图所示,已知双曲线以长方形
的顶点
,
为左、右焦点,且双曲线过
,
两顶点.若
,
,则此双曲线的标准方程为________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57dfc9d1109fe41145cc892b5702d9fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddae1423bd8fbb05d671234c14180272.png)
![](https://img.xkw.com/dksih/QBM/2019/5/17/2205498567966720/2205596892790784/STEM/2a2bef6e17d7412a857b4f2c776fa60f.png?resizew=193)
您最近一年使用:0次
2016-12-02更新
|
1423次组卷
|
8卷引用:北京师范大学遵义附属学校2020-2021学年高二下学期第一次月考数学(文)试题
北京师范大学遵义附属学校2020-2021学年高二下学期第一次月考数学(文)试题(已下线)2012-2013学年甘肃省兰州一中高二上学期期末考试数学试卷步步高高二数学暑假作业:【文】作业16 双曲线、抛物线步步高高二数学暑假作业:【理】作业16 双曲线、抛物线人教A版(2019) 选择性必修第一册 过关斩将 第三章 圆锥曲线的方程 3.2 双曲线 3.2.1 双曲线及其标准方程厦门市国祺中学2020-2021学年高二上数学第一次月考试题(已下线)3.2.1 双曲线及其标准方程-2020-2021学年高二数学课时同步练(人教A版选择性必修第一册)(已下线)3.2.1双曲线的标准方程(备作业)-【上好课】-2021-2022学年高二数学同步备课系列(苏教版2019必修第一册)
10-11高二下·河北石家庄·阶段练习
名校
解题方法
7 . 已知双曲线
的离心率为
,过点
和
的直线与原点的距离为
.
(1)求双曲线C的方程;
(2)直线
与该双曲线C交于不同的两点C,D,且C,D两点都在以点A为圆心的同一圆上,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18483c9c195ecd922772527fa85c0fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaf082502021e60d028a476c8a1ff22a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d04015890783f6b8b0264b1d1c9127.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求双曲线C的方程;
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3c8c0be780f3822c8615df3a1f02736.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2016-11-30更新
|
984次组卷
|
4卷引用:贵州省遵义求是高级中学2018-2019高二下学期月考数学(理)试题
贵州省遵义求是高级中学2018-2019高二下学期月考数学(理)试题(已下线)2010-2011年河北省正定中学高二下学期第一次月考数学理卷四川省威远中学2017-2018学年高二下学期期中考试数学(文)试题2.2.2双曲线的简单几何性质(习题)-2021-2022学年高二上学期数学北师大版(2019)选择性必修第一册