名校
解题方法
1 . 在平面直角坐标系中,已知点A坐标为
,若动点P位于y轴右侧,且到两定点
,
的距离之差为定值4,则
周长的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c865504bae15a800afe6fa5b635d7820.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08f24ad677d24612c937448cb583614d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3377c0c2bcd334a93133cdd37f34ed88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa65e9e7125c4bd360cf71ea4439e2c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
2 . 已知双曲线
的左、右焦点分别为
,直线
与双曲线交于
两点(点
在第一象限),且
,若
,则下列结论正确的是( )
![](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/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1fedcf44928a090ad5553edf8a0fd7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c48ef73ae947fdedfdc6500ea0d82f0.png)
A.双曲线的离心率为![]() |
B.双曲线的渐近线方程为![]() |
C.![]() |
D.若点![]() ![]() ![]() |
您最近一年使用:0次
2024-06-02更新
|
471次组卷
|
2卷引用:甘肃省张掖市某校2023-2024学年高三下学期模拟考试数学试题
名校
3 . 已知点
,
分别为双曲线
的左、右焦点,点A为C的右顶点,点P为C右支上的动点,记
,
分别为
,
内切圆半径.若
,
,
成等差数列,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3ec1ff9f2eb61dcce94f093c64b9c2a.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/0dad0c75ce33673ec4c425896e8619e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2858005b9ae89ae080d83dcc13cf8e81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3e95410f3b4fcb0cba425b521d1f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05dbb85151ab76cf6452c851f53f2d8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/246482388ea686b373fc1ad3e18347be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4ef569668e797b1e94257fd5f4384dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cdfc6a59392d1ac3cd89ddc0308864c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96fa27f8db6167d4802a510371077bb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3ec1ff9f2eb61dcce94f093c64b9c2a.png)
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名校
解题方法
4 . 已知点
分别为双曲线
的左、右焦点,
为坐标原点,过点
且斜率为
的直线与两条渐近线分别交于
两点,与双曲线
在第一象限交于点
,且
为线段
的两个三等分点,则双曲线
的离心率为( )
![](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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2122e3f1e76a635e58e4d54aa594c552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da01a3abe1c9dc4e6283afa0dc1a0d39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.2 |
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5 . 在天文望远镜的设计中利用了双曲线的光学性质:从双曲线的一个焦点出发的入射光线经双曲线镜面反射后,反射光线的反向延长线经过双曲线的另一个焦点.如图,已知双曲线C:
的左、右焦点分别为
,
,M是C的右支上一点,直线l与C相切于点M.由点
出发的入射光线碰到点M后反射光线为MQ,法线(在光线投射点与分界面垂直的直线)交x轴于点N,此时直线l起到了反射镜的作用.若
,则C的离心率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177ae60ade0b7ac20e7bdc40eaa1ef5a.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/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93d7ddfd425ced97c2f5aae0667fb6bd.png)
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2024·全国·模拟预测
解题方法
6 . 已知双曲线
的左、右焦点分别为
,过点
的直线
交
的左支于
两点.若
(
为坐标原点),点
到直线
的距离为
,则
的离心率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96c4088276acdbede4781b2ebc466366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9699dfb31899f352c8f7d406bff8a0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60c900136d7c36c0bee9e125b6578983.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
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2024高三·全国·专题练习
解题方法
7 . 已知双曲线
的左焦点
、右焦点
分别为双曲线
的左、右顶点,过
的直线分别交双曲线
的左、右两支于点
,交双曲线
的右支于点
(与
不重合),
关于
的一条渐近线的对称点为
,且
与
的周长之差为2,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87e09a56c608e418a5128f3eb32940e6.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/b80c87c91534b4adc427105595670200.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47444b5fbc4252516d54263062e47c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5eb2485f90dbfd0dfd6e7d179a856f5.png)
A.双曲线![]() |
B.![]() ![]() |
C.过点![]() ![]() ![]() ![]() |
D.若直线![]() ![]() ![]() ![]() |
您最近一年使用:0次
名校
解题方法
8 . 已知双曲线
:
的左、右焦点分别为
,
.
是
上一点
在第一象限
,直线
与
轴交于点
,若
,且
,则
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/578832b5e2b61bf599918028e68da17f.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2015049cd170e89070ec78e4497d381a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a770cfb79a5d2e372147c725d38f3a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
9 . 已知
双曲线
的左、右焦点,点
在
上,设
的内切圆 圆心为
,半径为
,直线
交
于
,若
,
,
则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40f98254a6193566587a70c7d95fdabf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e4d134d16becbca6a0795013fc4c80.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/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede935419d69a161bb22fd513647da06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643ef7d761de0e794fc39937dc72ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28bb0760b806ef159e2282482a239753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8907690d9c4c23012d0a1cd52d2e8efc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51159984b2cb00f30b3986315019623.png)
A.![]() | B.圆心![]() |
C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
10 . 已知双曲线
的左、右焦点分别为
,
,过
的直线与
轴相交于点
,与
在第一象限的交点为
,若
,
,则
的离心率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/6084ffa3daae96883a544a4e927455cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17e72d4676abd9fdf6a8a896ec1a2f0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次