名校
解题方法
1 . 已知椭圆
的弦被点
平分,则这条弦所在的直线方程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb4717d7fa6d522090c5e949f650bd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29343388ca8b33dc98325e65382b38a0.png)
您最近一年使用:0次
2021-11-19更新
|
1332次组卷
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6卷引用:安徽省安庆市第二中学2020-2021学年高二上学期12月月考数学试题
安徽省安庆市第二中学2020-2021学年高二上学期12月月考数学试题山东省2021-2022学年高二11月“山东学情”期中联考数学试题(B)山东省2021-2022学年高二11月“山东学情”期中联考数学试题(A)河南省新蔡县第一高级中学2021-2022学年高二上学期11月月考数学(理科)试题(已下线)第20讲 椭圆的简单几何性质10种常见考法归类(2)(已下线)专题03 椭圆13种常见考法归类(2)
名校
解题方法
2 . 椭圆
内,过点
且被该点平分的弦所在的直线方程为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d12ebd10f6c0bcf98be52c32b107f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0bea681006f614f8a070e9c6a942c04.png)
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2021-11-12更新
|
1243次组卷
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14卷引用:安徽省蚌埠市第二中学2019-2020学年高二12月月考数学(文)试题
安徽省蚌埠市第二中学2019-2020学年高二12月月考数学(文)试题安徽省淮北市树人高级中学2023-2024学年高二上学期第一次阶段考试数学试题河北省沧州市第一中学2020-2021学年高二上学期第一次月考数学试题青海省湟川中学2020-2021学年高二下学期第一次月考数学(文)试题江西省赣州市定南中学2021-2022学年高二3月月考数学(理)试题福建省南平市建瓯市芝华中学2019-2020学年高二上学期期中数学试题甘肃省白银市会宁县第二中学2017-2018学年高二上学期期末考试数学(理)试卷陕西省西安中学2020-2021学年高二上学期期末数学(理)试题(已下线)专题07 点差法-2021年高考数学二轮复习解题技巧汇总(新高考地区专用)福建省南平市高级中学2021-2022学年高二上学期期中考试数学试题(已下线)第3章 圆锥曲线与方程(章末测试提高卷)-2021-2022学年高二数学同步单元测试定心卷(苏教版2019选择性必修第一册)四川省绵阳市绵阳第一中学2021-2022学年高二上学期期中数学试题广西梧州市藤县第六中学2021-2022学年高二上学期期末热身考试数学(文)试题广西梧州市藤县第六中学2021-2022学年高二上学期期末热身考试数学(理)试题
3 . 已知椭圆
:
,直线
不过原点
且不平行于坐标轴,
与
有两个交点
,
,线段
的中点为
.
(1)证明:直线
的斜率与
的斜率的乘积为定值;
(2)若
过点
,射线
与椭圆
交于点
,四边形
能否为平行四边形?若能,求此时直线
斜率;若不能,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1120d33fc1bd1adbbe8947b4abe1441.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fcafa170f74e9890c0e525e563891a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14e902eb263971b466d0fcd91c56b453.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
名校
解题方法
4 . 已知椭圆
过点
,且离心率为
.过点
的直线
与椭圆
交于
两点,
为坐标原点.
(1)求椭圆
的方程;
(2)设
为
的中点,当直线
的斜率为1时,求中点
的坐标;
(3)当
的面积为
时,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/437d98e623c3f118fe7856554fd6f842.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a812a9b58ccba331cfd21d244329af01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fa71aa2ea224669698850108751a71a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7294f5ae2a24ff42e84cd9773b2a7287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2021-04-11更新
|
404次组卷
|
3卷引用:安徽省淮南市兴学教育2023-2024学年高二上学期第二次月考模拟数学试题
安徽省淮南市兴学教育2023-2024学年高二上学期第二次月考模拟数学试题北京市海淀区中关村中学2020-2021学年高二上学期期末考试数学试题(已下线)3.1.2 椭圆的简单几何性质(精练)-2021-2022学年高二数学一隅三反系列(人教A版2019选择性必修第一册)
名校
解题方法
5 . 已知椭圆C经过点
,且与椭圆E:
有相同的焦点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/d1d42873-64e9-4f9b-8d99-c57f6bd6b420.png?resizew=178)
(1)求椭圆C的标准方程;
(2)点A,B在椭圆C上,且线段
的中点坐标为
,求直线
的斜率;
(3)若动直线
与椭圆C有且只有一个公共点P,且与直线
交于点Q,问:以线段
为直径的圆是否经过x轴上的定点M﹖若存在.求出定点M的坐标;若不存在.请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de261e9b4defbc0be6440397031a87b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e595c257e4c0ade90a9bbbf0e6b0d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/d1d42873-64e9-4f9b-8d99-c57f6bd6b420.png?resizew=178)
(1)求椭圆C的标准方程;
(2)点A,B在椭圆C上,且线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29343388ca8b33dc98325e65382b38a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(3)若动直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5bd66dd6d5e09ff0893a938aed56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
2021-03-27更新
|
208次组卷
|
3卷引用:安徽省安庆市第二中学2020-2021学年高二上学期12月月考数学试题
名校
6 . 在平面直角坐标系中,已知椭圆
.如图所示,斜率为
且过点
的直线
交椭圆
于
,
两点,线段
的中点为
,射线
交椭圆
于点
,交直线
于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/8d8c192d-81a3-495f-8068-a6c7cea71e70.png?resizew=165)
(1)求证:
;
(2)若
在射线
上,且
,求证:点
在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0296bd9900adcc311f59ad44e940b86f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6bdac20e214b2cb3bd07f8d4778dcca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2a5e336b6bcba6354fd366c892dd06.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba53065eb180a682305fddb95d14b62f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/093836f9680ca10fdedd509558a04836.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/8d8c192d-81a3-495f-8068-a6c7cea71e70.png?resizew=165)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afbfb495fce5401b8c84c6c659c7c0b1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3b3850563eedfa2f509fa373b9d30eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
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2021-03-21更新
|
701次组卷
|
4卷引用:安徽省池州市东至二中2020-2021学年高二下学期3月月考数学(理)试题
安徽省池州市东至二中2020-2021学年高二下学期3月月考数学(理)试题湘豫名校联考2020-2021学年高三(3月)理科数学试题(已下线)专题1.11 圆锥曲线-定点、定值、定直线问题-2021年高考数学解答题挑战满分专项训练(新高考地区专用)江西省萍乡市2022届高三第一次质量检测数学(理)试题
名校
解题方法
7 . 椭圆
的离心率是
,过点
作斜率为k的直线l,椭圆E与直线l交于A,B两点,当直线l垂直于y轴时
.
(1)求椭圆E的方程;
(2)若点M的坐标为
,
是以
为底边的等腰三角形,求k的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22840186db0afc0e2b2e8915ce79b998.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a07468040d336edcb4badb29bacbce23.png)
(1)求椭圆E的方程;
(2)若点M的坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db20480adba69280e48944f0d15bba68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/822b3850f7df506efc1a592d57ec3a5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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名校
解题方法
8 . 椭圆C:
,则以点
为中点的弦所在直线方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a7315208b83923a2bddaae013f7a6e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d13ed5f4508ba44b95b7da1a2397b92d.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
9 . 抛物线
的顶点在原点,焦点
与双曲线
的右焦点重合,过点
且斜率为
的直线
与抛物线
交于
两点.
(1)求弦长
;
(2)求弦
中点到抛物线准线的距离.
![](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/335caead9a9e7d18587492828f7c2456.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d56ab70e602f2e2e291df643ab209162.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.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)
(1)求弦长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
(2)求弦
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2021-01-16更新
|
114次组卷
|
2卷引用:安徽省安庆市怀宁中学2020-2021学年高二(普通班)上学期第二次质量检测文科数学试题
名校
解题方法
10 . 已知
,
是椭圆
:
(
的左、右焦点,过
的直线
与椭圆
交于
,
两点,
为
,
的中点,直线
的斜率为
.
(1)求椭圆
的方程;
(2)过椭圆
的右焦点
的直线
与椭圆
分别相交于
,
两点,且与圆
:
相交于
,
两点,求
的取值范围.
![](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/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39973e0bc315af3c4c6f2d12329926ce.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.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/84fb85c78522640bcaf889f89ad89de9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
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