解题方法
1 . 已知双曲线
:
(
)与双曲线
有相同的渐近线.
(1)求双曲线
的方程;
(2)已知点
,点
,
在双曲线
的左支上,满足
,证明:直线
过定点;
(3)在(2)的条件下,求点
到直线
距离的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3701eb3f84adf1a7c997395f43c37344.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c0bb11f0edec2c5c005edf5dc464e71.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9c59f0e35b7ae5206e45878934482b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b765edba84cfb8d854c28972264e95dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
(3)在(2)的条件下,求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
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2024高三·全国·专题练习
解题方法
2 . 设双曲线C经过点(2 , 2), 且与
具有相同渐进线, 则C的方程为__________ ;渐进线方程为____________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfb1b9a8400b9ceb7a2e7497c8e5736c.png)
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解题方法
3 . 已知双曲线
的右焦点为
,一条渐近线的方程为
,若直线
与
在第一象限内的交点为
,且
轴,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b9f0b9e53a83e68f5fec944f343119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.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/08b1da9046b4cb82135a4a1eaa528c53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
解题方法
4 . 过双曲线
的右焦点作直线
与该双曲线交于
两点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1983309686915252c4efc8e4455b9d96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
A.与该双曲线有相同渐近线且过点![]() ![]() |
B.仅存在一条直线![]() ![]() |
C.若![]() ![]() ![]() |
D.若直线![]() ![]() ![]() |
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名校
解题方法
5 . 已知点在双曲线
的图像上.
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49cba284d675a3028d7a8d54f1f8ae70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)是否存在这样的双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/774c201bcb9fb3bad9d687803997b594.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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解题方法
6 . 已知双曲线
与双曲线
的渐近线相同,且M经过点
,N的焦距为 4.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/19/1f495925-c093-400f-8a1b-e8ad3bbb6c24.png?resizew=138)
(1)求M和N 的方程;
(2)如图,过点
的直线
(斜率大于0)与双曲线 M和N 左、右两支依次相交于点 A,B,C,D,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e47d5a14afa929b0f420506a4998f6e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0c97cdfbccfac205f7b826a73d3579a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb82d47413f946df419e18f5ba6fccd2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/19/1f495925-c093-400f-8a1b-e8ad3bbb6c24.png?resizew=138)
(1)求M和N 的方程;
(2)如图,过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f134c358bb5b5fa06c935a47c4ebf10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cd82bf82c3254c27b00f65b9a697e0d.png)
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2024-03-19更新
|
220次组卷
|
2卷引用:青海省海南州贵德高级中学2024届高三七模(开学考试)数学(理科)试题
解题方法
7 . 已知双曲线
的左右焦点分别为
,渐近线方程为
,且经过点
.
(1)求双曲线
的方程;
(2)过点
作双曲线
的切线
与
轴交于点
,试判断
与
的大小关系,并给予证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b75308335340230171130238f4dc6c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c4772d5a4460e4272b814498eb28439.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff58702fa978040dc5b2a8a5c19304c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc9c1cf5319d34e9de626dd631fc9cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3c8ebb29bd8db3655d5c4b40c66b9c3.png)
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解题方法
8 . (1)已知双曲线的一条渐近线方程是
,焦距为
,求双曲线的标准方程.
(2)求以双曲线C:
的焦点为顶点,顶点为焦点的椭圆标准方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4541bd6a12515d83b3a2ba8378fed1d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38acfaa0f912c2598cc341ec98da8a08.png)
(2)求以双曲线C:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a0bd4bd9985f1e367c100b453ed03f.png)
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2024高二·全国·专题练习
解题方法
9 . 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高二·全国·专题练习
解题方法
10 . 根据条件分别求双曲线的标准方程:
(1)与双曲线
有共同渐近线,且过点
;
(2)与椭圆
有相同的焦点,其中一条渐近线为直线
.
(1)与双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c58fa4a337f0b81b991fb32e8e6e3c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c51a57e05032acb94d05a0cbcaaa5fc.png)
(2)与椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c763113a1fc48e8acc83787b8cd24eec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45cc81cfaccc00aa4b7139de5a35a102.png)
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