名校
解题方法
1 . 已知双曲线
的渐近线方程为
,过
的右焦点
的直线交双曲线右支于
,
两点,
的内切圆分别切直线
,
,
于点
,
,
,内切圆的圆心为
,半径为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d425a7131017df2ef6eb55cc7070caf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dec7f6309562276a49560c17c98dedf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ff8a5886e42095da57422c8777c10d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f80ecb6b5d5eca464b3f099513c08fc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b283e4d7375d770823775e4036c9f6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
A.![]() ![]() | B.切点![]() ![]() |
C.![]() | D.![]() |
您最近一年使用:0次
解题方法
2 . 已知双曲线
的一个焦点为
为坐标原点,点
在双曲线上运动,以
为直径的圆过点
,且
恒成立,则
的离心率的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/844a1c77cdc51fb57f2fc55d791ea64f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09224287f31db61f4335560cdaf28ae3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ed568f7b6490ebbb104d105dbc07f6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次
名校
解题方法
3 . 已知双曲线
:
的左、右焦点分别为
,
,过
的直线与
的右支交于
,
两点,且
,若
,则双曲线
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.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/2a30f3a8b673cc28bd90c50cf1a35281.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/f65fbabf8abcfa336cf73304f7565896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5467d520121a4b201bd6f81972374431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
4 . 在平面直角坐标系
中,已知双曲线
的左、右焦点分别为
,
,点P在C上,且
,
,则C的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.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/6379894c4e00a91a991a6796179142a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a08170201ed74aa40a2d17046c953e74.png)
A.![]() | B.![]() | C.3 | D.2 |
您最近一年使用:0次
2024-06-11更新
|
686次组卷
|
2卷引用:山东省济南市2024届高三下学期高考针对性训练(5月模拟)数学试题
名校
解题方法
5 . 已知双曲线
的左、右焦点分别为
,根据双曲线的光学性质可知,过双曲线
上任意一点
的切线
平分
.直线
过
交双曲线
的右支于A,B两点,设
的内心分别为
,若
与
的面积之比为
,则双曲线
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c29bab2a74ca02d30e0deed068b042f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bac2f7fe4411d15bdeb4a72e98ea766e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94fe48bf7af022ecbbe13833fdcc2c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.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/6b1bd8fd746ffacd779249f171d80168.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e1fcb61ab66a7f514b7bad31d1e2f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ed517e1f28671f9dac3264ced2720a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e68113ebf789709f8a98d9e5f2f8a31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac97e6740365c85ad857aff85cefbe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-06-11更新
|
565次组卷
|
3卷引用:山东省济宁市2024届高三下学期三模数学试题
名校
解题方法
6 . 已知双曲线
,直线
是双曲线
的一条渐近线,则该双曲线的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2105999d86d0256b5fb90f814b305f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4407788e4dc88210bca71a2551d4f2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-06-08更新
|
248次组卷
|
2卷引用:2024届山东省德州市第一中学高三三模数学试题
名校
解题方法
7 . 已知双曲线
:
,O为坐标原点,
、
分别为
的左、右焦点,点P在双曲线上,且
轴,M在
外角平分线上,且
.若
,则双曲线的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0803835d6f594a60bd16c823e3ad2cd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acabb9b0fd26d09d514fb62cd19a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/766dd769370cddb4766cf202ab5b3928.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e796556a21c6b64d32313ef6c2a6e75e.png)
A.![]() | B.![]() | C.2 | D.![]() |
您最近一年使用:0次
2024-06-04更新
|
401次组卷
|
2卷引用:2024届山东省五莲县第一中学高三模拟预测数学试题
8 . 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)
您最近一年使用:0次
名校
解题方法
9 . 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
10 . 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