1 . 已知曲线
,下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c41ee28bc6a90e14289ff3f134027e56.png)
A.若曲线![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.当![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
您最近一年使用:0次
2023-02-06更新
|
360次组卷
|
2卷引用:江苏省扬州中学教育集团树人学校2022-2023学年高二下学期期初考试数学试题
名校
解题方法
2 . 已知
,
,点
满足
,记点
的轨迹为曲线
.斜率为
的直线
过点
,且与曲线
相交于
,
两点.
(1)求斜率
的取值范围;
(2)在
轴上是否存在定点
,使得无论直线
绕点
怎样转动,总有
成立?如果存在,求点
的坐标;如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3dac826c7d5c7ed6977e4a6b25c9b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4c9b615211b0d18f57333cd4590906c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76ceef7c000b8860839e98abaf47c8dd.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/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)求斜率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec14e8f5a0b164aa824a88641a5aeac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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2023-01-15更新
|
409次组卷
|
3卷引用:江苏省泰州市兴化市第一中学2022-2023学年高二下学期期初考试数学试题
名校
3 . “黄金双曲线”是指离心率为“黄金分割比”的倒数的双曲线(将线段一分为二,较大部分与全长的比值等于较小部分与较大部分的比值,则这个比值称为“黄金分割比”),若黄金双曲线
的左右两顶点分别为
,虚轴上下两端点分别为
,左右焦点分别为
,
为双曲线任意一条不过原点且不平行于坐标轴的弦,
为
的中点.设双曲线
的离心率为
,则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3db0cc24753f6ea44c19c3cc49e26024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d468be20b4d43f5de75416de20e8ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
A.![]() |
B.![]() |
C.直线![]() ![]() |
D.![]() |
您最近一年使用:0次
2023-01-13更新
|
799次组卷
|
6卷引用:高二数学开学摸底考02(江苏专用)-2023-2024学年高中下学期开学摸底考试卷
(已下线)高二数学开学摸底考02(江苏专用)-2023-2024学年高中下学期开学摸底考试卷江苏省盐城中学2022-2023学年高二上学期期末数学试题江苏省江苏省南京人民中学、南通海安市实验中学2023-2024学年高二上学期10月月考数学试题江苏省镇江市镇江中学2023-2024学年高二上学期期中数学试题湖北省恩施州巴东县第一高级中学2023-2024学年高二上学期末数学试题黑龙江哈尔滨市第一二二中学-202届高三一模数学试题
名校
解题方法
4 . 已知双曲线
的左、右顶点分别是
且经过点
,双曲线的右焦点
到渐近线的距离是
,不与坐标轴平行的直线
与双曲线交于
两点(异于
),
关于原点
的对称点为
.
(1)求双曲线
的标准方程;
(2)若直线
与直线
相交于点
,直线
与直线
相交于点
,证明:在双曲线上存在定点
,使得
的面积为定值,并求出该定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19a2dfac4003e486e875d81f273c7964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/663368000ac90f582d12675aa2d1e832.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e3ccc38868099bc4d542e00e0b66685.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b1b15a4605fce993cb13aefbf40360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/663368000ac90f582d12675aa2d1e832.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0276df41cac9dd65cdb868dad13d17e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec18c028746b73be7503ff6ff458a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be99fa94a1f3e4964fcc13a14fab9ba5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f448e533d1c16190db42123fe30b8358.png)
您最近一年使用:0次
2022-11-22更新
|
457次组卷
|
4卷引用:江苏省南通市海安高级中学2022-2023学年高二上学期开学数学试题
解题方法
5 . 在平面直角坐标系
中,已知点
,
,点
满足
,记点
的轨迹为
.
(1)求
的方程;
(2)已知
,
是经过圆
上一点
且与
相切的两条直线,斜率分别为
,
,直线
的斜率为
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed42ce3af95877426d1f6d66be3481d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f617bf7e538d8bb584c66cef0830b834.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf937fabdaeebdd6db8bfcbcdd7394e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bc12c55f2676aeb4f696f4a84e4d65b.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/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed1e9cdd5a82f29ec89b2c53b4fa6f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bc46772d71fb60910de6b8b157733e3.png)
您最近一年使用:0次
2022-03-30更新
|
1035次组卷
|
4卷引用:江苏省盐城市响水县灌江高级中学2022-2023学年高二下学期期初考试数学试题
江苏省盐城市响水县灌江高级中学2022-2023学年高二下学期期初考试数学试题江苏省南通市海安市2021-2022学年高二上学期期末数学试题(已下线)2.8直线与圆锥曲线的位置关系(2)(已下线)第10讲 高考难点突破二:圆锥曲线的综合问题(定值问题) (精讲)
名校
解题方法
6 . 在平面直角坐标系
中,已知过点
的直线
与双曲线
交于
、
两点,与
轴交于点
,且
,
.
(1)当点
在第一象限且
时,求直线
的方程;
(2)求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a54b5669e303d494def8a29bbb9c74e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c41c95e0a80f48f75b0bff3dab49d00e.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fc1cc1a0162c30db5e858c971866d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74dc616cea7720c39876cf0e99088c55.png)
(1)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdfec4233214c3a729c843dee0d186db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
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名校
解题方法
7 . 双曲线C:
-
=1(a>0,b>0)的离心率为
,虚轴长为2.
(1)求C的方程;
(2)设C的左、右焦点分别为F1,F2,S为y轴上一点,直线SF1和SF2与分别与C的左、右支交于P,Q两点,且满足∠F1PF2和∠F1QF2两角的角平分线互相垂直,求满足条件的所有点S坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7355be4fcbc3130a5951364a3be76d6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5268413295580cfda0755ab458b36b64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18483c9c195ecd922772527fa85c0fcb.png)
(1)求C的方程;
(2)设C的左、右焦点分别为F1,F2,S为y轴上一点,直线SF1和SF2与分别与C的左、右支交于P,Q两点,且满足∠F1PF2和∠F1QF2两角的角平分线互相垂直,求满足条件的所有点S坐标.
您最近一年使用:0次
名校
解题方法
8 . 双曲线
,过定点
的两条垂线分别交双曲线于
、
两点,直线
恒过定点______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9407dd040f0fc6216e18f9b28bc45d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0929421a6188c3122442866b0b85a5e.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/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
名校
解题方法
9 . 在平面直角坐标系xOy中,动点Р与定点F(2,0)的距离和它到定直线l:
的距离之比是常数
,记P的轨迹为曲线E.
(1)求曲线E的方程;
(2)设过点A(
,0)两条互相垂直的直线分别与曲线E交于点M,N(异于点A),求证:直线MN过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d599059e6b2c918ab15ee22611b6962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18483c9c195ecd922772527fa85c0fcb.png)
(1)求曲线E的方程;
(2)设过点A(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
您最近一年使用:0次
2021-12-05更新
|
1942次组卷
|
8卷引用:江苏省南京市建邺高级中学2022-2023学年高二下学期期初数学试题
江苏省南京市建邺高级中学2022-2023学年高二下学期期初数学试题江苏省连云港市东海县2021-2022学年高二上学期期中数学试题广东省广州市第六十五中学2022-2023学年高二上学期期末数学试题广东省广州市广东实验中学越秀学校2023-2024学年高二下学期3月月考数学试题(已下线)专题9-3 圆锥曲线压轴大题五个方程框架十种题型-2022年高考数学毕业班二轮热点题型归纳与变式演练(全国通用)(已下线)第09讲 高考难点突破一:圆锥曲线的综合问题(定点问题) (精讲)-1(已下线)专题31 圆锥曲线的垂直弦问题-1(已下线)重难点突破08 圆锥曲线的垂直弦问题 (八大题型)