解题方法
1 . 已知
,
是双曲线C:
的左右焦点,过
作双曲线C的一条渐近线的垂线,垂足为N,直线
与双曲线C交于点
,且
均在第一象限,若
,则双曲线C的离心率是________ .
![](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/a5ec7fa23be9cbe9a50607ea6bc8a4ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfbdbe9a17a23c44cec8c7475c4dc1a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef02d2d4013d3d82a7eea017f17bca93.png)
您最近一年使用:0次
名校
解题方法
2 . 已知双曲线
:
的右顶点,右焦点分别为A,F,过点A的直线l与C的一条渐近线交于点P,直线PF与C的一个交点为Q,
,且
,则C的离心率为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50c857dc9f7befdcc69d64cf96860969.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5341177a9587281d5ebb28807ee023a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37375c00701dfa46e62ab52e81e65388.png)
您最近一年使用:0次
2024-03-06更新
|
155次组卷
|
3卷引用:浙江省临平萧山联考2023-2024学年高二上学期期末数学试题
名校
解题方法
3 . 已知
为双曲线
:
上位于第一象限内一点,过点
作x轴的垂线,垂足为
,点
与点
关于原点对称,点
为双曲线
的左焦点,则( )
![](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/e9a0bd4bd9985f1e367c100b453ed03f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.![]() |
D.![]() |
您最近一年使用:0次
2023-11-17更新
|
1326次组卷
|
5卷引用:浙江省台州市2024届高三上学期第一次教学质量评估数学试题
名校
解题方法
4 . 已知双曲线C:
的左焦点为F,P为C右支上的动点,过P作C的一条渐近线的垂线,垂足为A,O为坐标原点,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5dae637ca6fdc4d2480fb2cef387500.png)
A.点F到C的一条渐近线的距离为2 |
B.双曲线C的离心率为![]() |
C.则P到C的两条渐近线的距离之积大于4 |
D.当![]() ![]() ![]() |
您最近一年使用:0次
2023-11-19更新
|
654次组卷
|
6卷引用:浙江省湖州市第二中学2024届高三上学期期中数学试题
5 . 在直角坐标系
中,
是双曲线
的两条渐近线上的动点,满足点A在第一象限,点
在第四象限,且直线
与
的右支有交点.
(1)求
的最小值;
(2)设
是直线
与
的一个交点且
.记
上的点到
的焦点的距离的取值集合为S,若
,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0017262e45089093f70001cae2c60257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba4d488d56b95a44a6b0b40d3e89c010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0da8a341058083ab6ee318b4107b43da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
您最近一年使用:0次
名校
解题方法
6 . 已知双曲线
的左、右焦点分别为
,且
到
的一条渐近线的距离为
.
(1)求
的方程;
(2)过
的左顶点且不与
轴重合的直线交
的右支于点
,交直线
于点
,过
作
的平行线,交直线
于点
,证明:
在定圆上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24d6b900707783424bc28f1c148ba049.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b650820d7bed48ed67a2869ad8c65ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3656055f5256cd06e636ea96e9f89c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
2023-04-15更新
|
1522次组卷
|
6卷引用:浙江省绍兴市2023届高三下学期4月高考适应性考试(二模)数学试题
浙江省绍兴市2023届高三下学期4月高考适应性考试(二模)数学试题(已下线)专题07 平面解析几何(已下线)押新高考第21题 圆锥曲线广东省广州市从化区从化中学2023届考前仿真模拟1数学试题(已下线)专题3-4 双曲线大题综合10种题型归类(讲+练)-【巅峰课堂】2023-2024学年高二数学热点题型归纳与培优练(人教A版2019选择性必修第一册)(已下线)专题06 圆锥曲线大题
22-23高二上·浙江绍兴·期末
解题方法
7 . 已知双曲线
与椭圆
的焦点相同,双曲线
的左右焦点分别为
,过点
的直线与双曲线
的右支交于
两点,
与
轴相交于点
,
的内切圆与边
相切于点
.若
,则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef66f4832adc43902055a7e6d258037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb4717d7fa6d522090c5e949f650bd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7638c88f01d609d79947033ed4ff36a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9f5f4ad0caac5a0fecb64f3908d2290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/246482388ea686b373fc1ad3e18347be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/236f52e04ddbd7253f44b97c4756ef9c.png)
A.双曲线![]() ![]() |
B.过点![]() ![]() |
C.点![]() ![]() ![]() |
D.若![]() ![]() ![]() |
您最近一年使用:0次
8 . 已知双曲线
,点A,B在双曲线右支上,O为坐标原点.
(1)若过点A作双曲线的两条渐近线的平行线,分别交两条渐近线于点M,N,证明:平行四边形
的面积为定值;
(2)若
,D为垂足,求点D的轨迹的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c477e5ade921ffa8377c4719319380ff.png)
(1)若过点A作双曲线的两条渐近线的平行线,分别交两条渐近线于点M,N,证明:平行四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f2cf7996e3462e9791940885d3a5563.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dd436ca3680ce9f9cba4b052ccdd9c7.png)
您最近一年使用:0次
2023-02-27更新
|
516次组卷
|
3卷引用:浙江省台州市2022-2023学年高二上学期2月期末数学试题
解题方法
9 . 已知双曲线
,焦点
到其中一条渐近线的距离为
.
(1)求
;
(2)动点M,N在曲线C上,已知点
,直线
分别与y轴相交的两点关于原点对称,点Q在直线
上,
,证明:存在定点T,使得
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e470d2e57700d049e4034fa57540f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)动点M,N在曲线C上,已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06ebd2da016e7029c4dd72b9e377190c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d42cb68c5c877a455ba7ac0a6b6a651.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bcb0ddbec070df305979a2a87d4ee3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e8a95da2004dcb52f563e958496c676.png)
您最近一年使用:0次
名校
解题方法
10 . 已知双曲线,过双曲线C上任意一点P作两条渐近线的垂线,垂足分别为M,N,则
的最小值为
您最近一年使用:0次
2022-12-27更新
|
616次组卷
|
5卷引用:浙江省杭州学军中学2022-2023学年高二上学期12月教学质量检测数学试题
浙江省杭州学军中学2022-2023学年高二上学期12月教学质量检测数学试题上海市向明中学2022-2023学年高二下学期期中数学试题(已下线)考点18 解析几何中的范围、最值问题 2024届高考数学考点总动员(已下线)专题12 双曲线的几何性质8种常见考法归类(3)(已下线)通关练16 双曲线13考点精练(100题)- 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第一册)