1 . 已知
是双曲线
的右焦点,过点F的直线
与E交于
两点(不同于E的顶点),当直线
过点
时,C恰为
的中点.
(1)求E的方程;
(2)设
分别为E的左、右顶点,
与
交于点
与
交于点Q,若D为
的中点,证明
为定值,并求出该定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63309dbc3612815f6dbdee23d9a10adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef66f4832adc43902055a7e6d258037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46aa4df64b8827cfd81e4c91560b4b1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(1)求E的方程;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62d001b03344e172f30a9a073562ecf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d8c7cecf22a165d1cb6d9e89dd0a1c.png)
您最近一年使用:0次
名校
解题方法
2 . 已知双曲线
的右焦点
,离心率为
,过F的直线
交
于点
两点,过
与
垂直的直线
交
于
两点.
(1)当直线
的倾斜角为
时,求由
四点围成的四边形的面积;
(2)直线
分别交
于点
,若
为
的中点,证明:
为
的中点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be92f0e0012a7696c78e3e00513edefd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18483c9c195ecd922772527fa85c0fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
(1)当直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f63a76a5f78eb64e64b5a2c9f1553cb.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba91671bbed8491d9116eac21dc65618.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
您最近一年使用:0次
2024-04-08更新
|
946次组卷
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4卷引用:河南省信阳市新县高级中学2024届高三数学考前仿真冲刺卷
名校
解题方法
3 . 已知双曲线
的焦点
到一条渐近线
的距离为
.
(1)求
的方程;
(2)若直线
交双曲线
于
两点,
是坐标原点,若
是弦
的中点,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/225af894f3155152ebdb0cecdcd42495.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/920fdf4cd0153c43eb7b9130b86de598.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0074b77c66776e4e7c70e2f0db15fbe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
您最近一年使用:0次
2024-02-28更新
|
348次组卷
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2卷引用:河南省新高中创新联盟TOP二十名校2023-2024学年高二下学期2月调研考试数学试题
解题方法
4 . 已知点
是离心率为2的双曲线
上的三点,直线
的斜率分别是
,点
分别是线段
的中点,
为坐标原点,直线
的斜率分别是
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbcf744dceb18820e4a1ca354cb3cfe1.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce5d2e7f7ed678e14e2c1d1297cef34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942e6dafcfcbf0682856b9f25178694d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dca1726d463bd741c904abd9b6589056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/927456b0989846a2f1573844bbaa2105.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942e6dafcfcbf0682856b9f25178694d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12e8ebdbd58b757fc18d53f7a57348ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9025c0d32f94373105c73ff3f80c6be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a8a96ae139699a6032c76f5026ee2aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbcf744dceb18820e4a1ca354cb3cfe1.png)
您最近一年使用:0次
5 . 已知双曲线
的右焦点为
,过点
且斜率为3的直线与双曲线
分别交于
两点,若
是线段
的中点,且
,则双曲线的渐近线方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24550b13dbecf7d86c7054250e987274.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e29fa24a53fe0b89c6361baf8c37cc0.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2024-01-23更新
|
243次组卷
|
2卷引用:河南省信阳市宋基信阳实验中学2023-2024学年高二上学期期末复习数学测评卷(五)
6 . 已知双曲线
:
的一个焦点为
,一条渐近线方程为
,
为坐标原点.
(1)求双曲线
的标准方程;
(2)已知倾斜角为
的直线
与双曲线
交于
两点,且线段
的中点的纵坐标为4,求弦长
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ec7fa23be9cbe9a50607ea6bc8a4ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67eb0080af1b3ac6d3d29fd26ba8a01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0f7fbfa2214ca72495a993b2fed8b61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知倾斜角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/534de19db99087b564cd3e9ac4c4568c.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
您最近一年使用:0次
2023-12-21更新
|
2118次组卷
|
8卷引用:河南省信阳市信高教育集团南湾校区2023-2024学年高二上学期期末复习检测数学试题(一)
河南省信阳市信高教育集团南湾校区2023-2024学年高二上学期期末复习检测数学试题(一)河南省信阳市固始县高级中学第一中学2023-2024学年高二上学期第三次月考数学试题山东省潍坊市2023-2024学年高二上学期普通高中学科素养能力测评数学试题(已下线)模块三 专题6 大题分类练(圆锥曲线)拔高能力练 期末终极研习室(高二人教A版)(已下线)专题04 双曲线15种常见考法归类(4)四川省宜宾市叙州区第一中学校2023-2024学年高二上学期期末数学试题山东省烟台市爱华高级中学2023-2024学年高二上学期期末模拟数学试题(二)A卷(已下线)专题03 圆锥曲线的方程(2)
解题方法
7 . 已知动点P到点
的距离是到直线
的距离的
倍,记动点P的轨迹为曲线
.
(1)求
的方程;
(2)过点
能否作一条直线l,使得l与
交于B,C两点,且A是线段BC的中点?若存在,求出直线的方程;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808bbc02ef2deaee8a8ff39610832b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e102c52a414398b755ce675a09dd9eb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9c59f0e35b7ae5206e45878934482b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
您最近一年使用:0次
2023-12-20更新
|
453次组卷
|
4卷引用:河南省九师联盟2024届高三上学期12月质量检测数学试题
名校
解题方法
8 . 如图,双曲线
的左右顶点为
,
,
为
右支上一点(不包含顶点),
,
,
,直线
与
的渐近线交于
、
,
为线段
的中点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62fbb99f1f9771c64e2232d27876ca6b.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/482002db587fa5dcc33454ebe5ace500.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec3fcca37520855783dc1295b16f40b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef6ab2d197160f40b72fe0abb3fe527d.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
A.双曲线![]() ![]() | B.![]() ![]() |
C.![]() | D.若直线![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2023-12-07更新
|
1186次组卷
|
4卷引用:河南省信阳市2023-2024学年高三上学期第二次教学质量检测数学试卷
河南省信阳市2023-2024学年高三上学期第二次教学质量检测数学试卷湖北省十一校2024届高三第一次联考数学试题(已下线)第5套 最新模拟重组精华卷5---模块一 各地期末考试精选汇编(已下线)河南省信阳市2023-2024学年高三上学期第二次教学质量检测数学试题变式题11-16
名校
解题方法
9 . 已知双曲线M:
与抛物线
有相同的焦点,且M的虚轴长为4.
(1)求M的方程;
(2)是否存在直线l,使得直线l与M交于A,B两点,且弦AB的中点为
?若存在,求l的斜率;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a29c0738fd840c1acadc91365ff366f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6fdedd1db38755989cd462c151f5106.png)
(1)求M的方程;
(2)是否存在直线l,使得直线l与M交于A,B两点,且弦AB的中点为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/530e5817131adf2c05b99ff18eb9060f.png)
您最近一年使用:0次
2023-11-09更新
|
650次组卷
|
2卷引用:河南省部分名校2023-2024学年高二上学期期中数学试题
10 . 中心在原点的双曲线
的焦点在x轴上,且焦距为4,请从下面3个条件中选择1个补全条件,并完成后面问题:
①该曲线经过点
;
②该曲线的渐近线与圆
相切;
③点
在该双曲线上,
,
为该双曲线的左、右焦点,当点
的纵坐标为
时,以
,
为直径的圆经过点
.
(1)求双曲线C的标准方程;
(2)过定点
能否作直线
,使
与此双曲线相交于
两点,且
是弦
的中点?若存在,求出
的方程;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
①该曲线经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aab000962b3e21db0bd949eb7a0d6fc.png)
②该曲线的渐近线与圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea31a691dd967aa83caf78e0a2e95d05.png)
③点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.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/ac047e91852b91af639feec23a9598b2.png)
(1)求双曲线C的标准方程;
(2)过定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/355dffb42861f3e297694f4be77c694c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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