1 . 双曲线
的虚轴长为2,
为其左右焦点,
是双曲线上的三点,过
作
的切线交其渐近线于
两点.已知
的内心
到
轴的距离为1.下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad8799160cd50d995db10675a83d4b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89fc107c4b33d6dd648b396156494ea9.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/01c74a907dda6bb7d9d56d009d9df253.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/d053b14c8588eee2acbbe44fc37a6886.png)
A.![]() ![]() |
B.当![]() ![]() ![]() |
C.当![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() |
您最近一年使用:0次
2022-04-07更新
|
3751次组卷
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6卷引用:湖北省二十一所重点中学2022届高三下学期第三次联考数学试题
湖北省二十一所重点中学2022届高三下学期第三次联考数学试题湖北省九校教研协作体2023届高三上学期起点考试数学试题(已下线)考点23圆锥曲线综合应用-2-(核心考点讲与练)-2023年高考数学一轮复习核心考点讲与练(新高考专用)(已下线)专题27 圆锥曲线与四心问题 微点5 圆锥曲线与四心问题综合训练湖南省怀化市第三中学2022-2023学年高二上学期期中数学试题(已下线)3.2.1 双曲线及其标准方程(重难点突破)-【冲刺满分】2023-2024学年高二数学重难点突破+分层训练同步精讲练(人教A版2019选择性必修第一册)
解题方法
2 . 已知双曲线C:
,
,
为C的左、右焦点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dad0c75ce33673ec4c425896e8619e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
A.双曲线![]() |
B.若P为C上一点,且![]() ![]() ![]() |
C.若直线![]() ![]() ![]() |
D.在C的左、右两支上分别存在点M,N使得![]() |
您最近一年使用:0次
3 . 如图所示,已知
是双曲线
右支上任意一点,双曲线
在点
处的切线分别与两条渐近线
交于
两点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c467a1b81cd28f9caf15414a3383399d.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c75eba5051fb2a61e0f5ac08e658d8e.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/d63f162c4846a76cadee56ae2f42e37c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c467a1b81cd28f9caf15414a3383399d.png)
![](https://img.xkw.com/dksih/QBM/2022/1/15/2895174291865600/2897201265590272/STEM/fa8a7d9b-4997-4a38-8e33-5fe3bed0f91f.png?resizew=187)
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名校
解题方法
4 . 已知
为坐标原点,双曲线
和椭圆
均过点
且以
的两个顶点和
的两个焦点为顶点的四边形是面积为
的正方形.
(1)求
,
的方程;
(2)是否存在直线
,使得
与
交于
,
两点,与
只有一个公共点,且
?证明你的结论;
(3)椭圆
的右顶点为
,过椭圆
右焦点的直线
与
交于
、
两点,
关于
轴的对称点为
,直线
与
轴交于点
,
,
的面积分别为
,
,问
是否为定值?若是,求出该定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd89df0f194cffb5b440e8c7f983cb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a258893e87121fc82b385e9a0c149ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75b5520d51d00cdf0d3adecc83faa62f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)是否存在直线
![](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/b1241216f3c1cb5e73043dd1037f556d.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/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f67c8e3d9a5e7713b6f5d6b0e8fbdb.png)
(3)椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a03c5e1e4e2669563b22dcf05bfb9b8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/467a7b2829ea7f2573865b43fd66d937.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a9dabb53dc826019fc8b6ae6d940c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
您最近一年使用:0次
2022-01-14更新
|
564次组卷
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4卷引用:天津市耀华中学2021-2022学年高三上学期第三次月考数学试题
名校
5 . 已知曲线C的方程为
,点
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ffb138fc843a9ef427273804c759e5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8748dc55e2f45bc37fc4d84d7310f79.png)
A.曲线C上的点到A点的最近距离为1 |
B.以A为圆心、1为半径的圆与曲线C有三个公共点 |
C.存在无数条过点A的直线与曲线C有唯一公共点 |
D.存在过点A的直线与曲线C有四个公共点 |
您最近一年使用:0次
2022-01-12更新
|
857次组卷
|
6卷引用:专题14 解析几何中的范围、最值和探索性问题(练)--第一篇 热点、难点突破篇-《2022年高考数学二轮复习讲练测(新高考·全国卷)》
(已下线)专题14 解析几何中的范围、最值和探索性问题(练)--第一篇 热点、难点突破篇-《2022年高考数学二轮复习讲练测(新高考·全国卷)》(已下线)江苏省盐城市、南京市2022届高三上学期1月第一次模拟考试数学试题变式题6-10重庆市2021-2022学年高二上学期期末数学试题浙江省精诚联盟2021-2022学年高二下学期3月联考数学试题福建省福州第三中学2021-2022学年高二上学期期末考数学试题(已下线)高二上学期期末【全真模拟卷02】-2022-2023学年高二数学考试满分全攻略(人教A版2019选修)
6 . 已知双曲线
的方程为
两点分别是双曲线
的左,右顶点,点
是双曲线
上任意一点(与
两点不重合),记直线
的斜率分别为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c232a5ee2b300cddab36247d16590ba.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
A.双曲线![]() |
B.若双曲线![]() ![]() |
C.![]() |
D.存在实数![]() ![]() |
您最近一年使用:0次
解题方法
7 . 1.已知点
,
,动点
满足直线
的斜率与直线
的斜率乘积为
.当
时,点
的轨迹为
;当
时,点
的轨迹为
.
(1)求
,
的方程.
(2)是否存在过
右焦点的直线
,满足直线
与
交于
,
两点,直线
与
交于
,
两点,且
?若存在,求所有满足条件的直线
的斜率之积;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850811ba59a05e945a665196539a048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80672dda9430cb42b3136bcb1b67bbad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13af018556f0b484ed38519f2edc791c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd0a96569d3ae91b7c61cbb8ba22a018.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de85df85401e7e8da683ea4a784963c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb6101e45f8d7013bc3dc4197188c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d1c567b22c69c1c96a5bb71181b7170.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acfc9319b4dfcefd8f0bb0338f7cbf2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb6101e45f8d7013bc3dc4197188c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acfc9319b4dfcefd8f0bb0338f7cbf2.png)
(2)是否存在过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb6101e45f8d7013bc3dc4197188c0c.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/afb6101e45f8d7013bc3dc4197188c0c.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acfc9319b4dfcefd8f0bb0338f7cbf2.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/0cd5dac19a3fa0ffa7f160275691ca70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
8 . 已知曲线
:
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7466c15c8b9011fbcbe88e594231c499.png)
A.直线![]() ![]() |
B.直线![]() ![]() |
C.当直线![]() ![]() ![]() ![]() ![]() ![]() |
D.当直线![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2021-10-22更新
|
1044次组卷
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3卷引用:广东省茂名市五校联盟2022届高三上学期第一次联考数学试题
名校
解题方法
9 . 在平面直角坐标系
中,双曲线
的左顶点到右焦点的距离是
,且
的离心率是
.
(1)求双曲线
的标准方程;
(2)点
是
上位于第一象限的一点,点
、
关于原点
对称,点
、
关于
轴对称.延长
至
使得
,且直线
和
的另一个交点
位于第二象限中.
(i)求
的取值范围;
(ii)证明:
不可能是
的三等分线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb57bb18755127be041d346444a4743e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5f1fd3a94cddf909fe40f7d21f28899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(ii)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac37366d2b54dc7d9a95ac6ddda5f3a8.png)
您最近一年使用:0次
10 . 已知双曲线
,
为双曲线上一点,过
点的切线为
,双曲线的左右焦点
,
到直线
的距离分别为
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dad0c75ce33673ec4c425896e8619e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca7faa3d6468fda497b7fdbe4ee30850.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5edf900c810371fb21297c15f86d8743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31ac1def558351e2e3ed1235c570530.png)
A.![]() |
B.直线![]() ![]() ![]() ![]() ![]() ![]() ![]() |
C.该双曲线的共轭双曲线的方程为![]() |
D.过![]() |
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