2024高三·全国·专题练习
1 . 已知双曲线C:
的一条渐近线方程为
,一个焦点到该渐近线的距离为
,则双曲线的方程为________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe33e1dda1b4b1d5a7fc3023837c53d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/222ae190a4191d5a8163e917496948bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9766dfef2a4159f49c7bd349fb36d670.png)
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解题方法
2 . 已知双曲线
:
的焦距为
,双曲线C的一条渐近线与曲线
在
处的切线垂直,M,N为
上不同两点,且以MN为直径的圆经过坐标原点
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1f676c51d88bc310b0e135122be4767.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ec7fa23be9cbe9a50607ea6bc8a4ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b10e8abf8690e4b129466ddb918bcc94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/843f14ca647a31197125e211e0ac5937.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea0f643d5b14c0bdb6e56ceaac1e56d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1f676c51d88bc310b0e135122be4767.png)
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解题方法
3 . 已知双曲线
的左、右焦点分别为
,
,渐近线方程为
,P为双曲线C上一点,且满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/472080ddc3a2a9c5355789bab235cfde.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e4e568d9cd57c442f011a787ab8aaf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914c2124260496e9307d6448c0c943f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b6bb019e2d7c6d17d15ec4d9043f5e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19973f8d5f144416fdac0e155b2467af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/472080ddc3a2a9c5355789bab235cfde.png)
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解题方法
4 . 已知双曲线
的一条渐近线平行于直线
,且双曲线的一个焦点在直线
上,则该双曲线的方程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0497127048425de426219514dcce135.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2024-04-10更新
|
384次组卷
|
4卷引用:河北省廊坊市香河县第一中学2023-2024学年高三下学期模拟考试数学试卷
名校
5 . 一双曲线过点
,一条渐近线的方程是
,则其标准方程是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ad98ebf7a3006722baf1ed6cf5fb666.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abeb57d8e728c8d9bd15e8902b70a80.png)
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解题方法
6 . 已知双曲线C的渐近线方程为
,两顶点为A,B,双曲线C上一点P满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4706acbdca5d7c24ea284ae052daad.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d3051f43ac48c0a730a791b8a93ad37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83995596fe930cbb2ce9c31f9a7f733d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4706acbdca5d7c24ea284ae052daad.png)
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解题方法
7 . 若双曲线
的一条渐近线为
,则过抛物线
的焦点且垂直于
轴的弦
,与抛物线的顶点组成的三角形的面积为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddb6db638d843af09ff4c190c466037e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23afc43a8c5b8cfe6bf2a1caed920c01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f773e2ceaff0e2c54b432b649f2411f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2024高二·全国·专题练习
解题方法
8 . 与双曲线
有公共的渐近线,且焦距为8的双曲线的标准方程为_______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/795d3c4d3b9ee412e43434fb5e6d1301.png)
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2024·全国·模拟预测
名校
解题方法
9 . 已知双曲线
:
的焦距为
,过双曲线
上任意一点
作直线
,
分别平行于两条渐近线,且与两条渐近线分别交于点
,
.若四边形
的面积为
,则双曲线
的方程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50fe7ad2404879870c9bf18bf03fdf2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b10e8abf8690e4b129466ddb918bcc94.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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.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/c40b8789cc8d81b3cf64f0b318ab982a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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2024-01-18更新
|
303次组卷
|
4卷引用:2024届数学新高考学科基地秘卷(八)
(已下线)2024届数学新高考学科基地秘卷(八)广东省广州市执信中学2024届高三上学期元月阶段测试数学试题(已下线)模块七 圆锥曲线(测试)黑龙江省牡丹江市第三高级中学2024届高三下学期高考前适应性演练数学试卷
解题方法
10 . 已知
是双曲线
的左,右焦点,
的一条渐近线
的方程为
,且
到
的距离为3,
为
的第一象限上的一点,点
的坐标为
为
的平分线,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/204196267ea8c9ec2544b3084d7952da.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f86bebdf5931efbdc627baa52f97392e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64dfdc4da53a7913b01647d751c77c8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94fe48bf7af022ecbbe13833fdcc2c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/204196267ea8c9ec2544b3084d7952da.png)
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