名校
解题方法
1 . 双曲线
的左顶点为A,右焦点为
,过点A且倾斜角为
的直线
顺次交两条渐近线和
的右支于
,且
,下列结论不正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3c8091d78595c42d437ff5766431a8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.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/0f94bfed76724054ae0ec4997914c08b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79016e5cebdaf32a36945bbfc404da02.png)
A.离心率为2 | B.![]() |
C.![]() | D.![]() |
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解题方法
2 . 在平面直角坐标系
中,过点
的直线
与双曲线
的两条渐近线相交于
两点,若线段
的中点是
,则
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18f4ec943ad1319d9df9ead145195817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6114ce586d4468f1b83c85bf029ba625.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
解题方法
3 . 设双曲线
的左、右顶点分别为
,
,左、右焦点分别为
,
,
,且
的渐近线方程为
,直线
交双曲线
于
,
两点.
(1)求双曲线
的方程;
(2)当直线
过点
时,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96c4088276acdbede4781b2ebc466366.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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e6418c268ad440341271e980fceb7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dec7f6309562276a49560c17c98dedf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)当直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ed24bfcc37b79fe9ca61ed8fdf26ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc5604d3e156df3e7ccca0ccec9c9d45.png)
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4 . 已知双曲线
,过实轴所在直线上任意一点
的弦的端点
与点
的连线所成的角被焦点所在的直线平分,即
,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b8c5d1ac937ed36b1090d3f259ea1f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d4ba1fa3c2844799756e3b50d52dd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fbd8e930408108eb4d41d74554f2ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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真题
解题方法
5 . 若直线
与双曲线
只有一个公共点,则
的一个取值为 ________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04e2007b599aacfaa55f52cc995500c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1892b7c3cd7bea116f532f66fba44662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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7日内更新
|
2312次组卷
|
7卷引用:2024年北京高考数学真题
2024年北京高考数学真题专题08平面解析几何(已下线)2024年北京高考数学真题变式题11-15专题11平面解析几何(第一部分)专题08[2837] 平面解析几何(已下线)五年北京专题08平面解析几何(已下线)三年北京专题08平面解析几何
2024高三·全国·专题练习
6 . 已知双曲线
,过点
作直线
,使
与
有且只有一个公共点,则满足条件的直线
共有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de66df5b4cd1344339588b99bf7214a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/847fea08d7cb36942bd5028b2cb7707e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
A.1条 | B.2条 | C.3条 | D.4条 |
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名校
解题方法
7 . 双曲线
,左、右顶点分别为A,B,O为坐标原点,如图,已知动直线l与双曲线C左、右两支分别交于P,Q两点,与其两条渐近线分别交于R,S两点,则下列命题正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
A.存在直线l,使得![]() |
B.当且仅当直线l平行于x轴时,![]() |
C.存在过![]() ![]() |
D.若直线l的方程为![]() ![]() |
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2024高三·全国·专题练习
8 . 过点
且与双曲线
有且只有一个公共点的直线有_________ 条,它们的方程分别是____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2d1841b904535ace5b1c91f6887f57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a86ccbd7791f91580f8ed589d137660.png)
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9 . 双曲线具有光学性质:从双曲线一个焦点发出的光线经过双曲线镜面反射,其反射光线的反向延长线经过双曲线的另一个焦点.如图,双曲线
的左、右焦点分别为
,从
发出的两条光线经过
的右支上的
两点反射后,分别经过点
和
,其中
共线,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8042b7ad208ff9de484fab4a56a41a9c.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.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/33bc58ac77b6b1dcbacd1c043484481f.png)
A.若直线![]() ![]() ![]() ![]() |
B.当点![]() ![]() ![]() ![]() ![]() |
C.当![]() ![]() |
D.当![]() ![]() |
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名校
10 . 已知双曲线
的一条渐近线方程为
,焦距为6,左顶点为
,点
是双曲线
的右支上相异的两点,直线AB,AC分别与直线
交于点
,且以线段
为直径的圆恰过双曲线
的右焦点
.
(1)求双曲线
的标准方程;
(2)求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef66f4832adc43902055a7e6d258037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25869dd14f3e7412beda491bb83f982d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40460e97733a56b0b9963f8c641c47c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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