名校
解题方法
1 . 在平面直角坐标系
中,已知椭圆
与直线
R),四个点
中有三个点在椭圆
上,剩余一个点在直线
上.
(1)求椭圆
的方程;
(2)若动点
在直线
上,过
作直线交椭圆
于
两点,使得
,再过
作直线
,求证:直线
恒过定点,并求出该定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a12012d9874b3913d262963ba12d11f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caa615898e91d546451cf0b538fb92d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若动点
![](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/dad2a36927223bd70f426ba06aea4b45.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/6b3384392c0eaabe04ae2aea7a3f2649.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47c866a0fafe19a2c353aa499c4a0658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
您最近一年使用:0次
解题方法
2 . 设椭圆
的离心率等于
,拋物线
的焦点
是椭圆
的一个顶点,
分别是椭圆的左右顶点.
(1)求椭圆
的方程;
(2)动点
为椭圆上异于
的两点,设直线
的斜率分别为
,且
,求证:直线
经过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ebaa32f4f1f4f807ca9aeb7fb29951.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9f5f4ad0caac5a0fecb64f3908d2290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ebaa32f4f1f4f807ca9aeb7fb29951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ddfa25e097562b856ddd5e7c0758ee2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c3071b3b063a35df2196580f20315ba.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
3 . 已知椭圆
过点
,且离心率为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/1906bdea-fb00-4310-862e-edc6e5be9c03.png?resizew=261)
(1)求椭圆
的方程;
(2)过
作斜率分别为
的两条直线,分别交椭圆于点
,且
,证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4614a53ea9e2902f823013e20e3b31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383f12cb70ca55eba4ff012771dbfa9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/1906bdea-fb00-4310-862e-edc6e5be9c03.png?resizew=261)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9ec084f0e202fc7e4c7a90fcae03501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61ef2e7c835443fcdc4c757e35d9e160.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ec7bcf5820dfe70290259c2d7ac1ea5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
2021-10-20更新
|
2452次组卷
|
8卷引用:黑龙江省大庆中学20201-2022学年高三上学期第一次月考数学(文)试题
黑龙江省大庆中学20201-2022学年高三上学期第一次月考数学(文)试题重庆市涪陵实验中学校2022届高三上学期期中数学试题湖南省长沙市宁乡市2021-2022学年高二上学期期末数学试题湖南省常德市淮阳中学2021-2022学年高二上学期期中数学试题(已下线)2022年全国高考乙卷数学(文)试题变式题13-16题(已下线)2022年全国高考乙卷数学(文)试题变式题21-23题江西省宜春市宜丰县宜丰中学创新部2022-2023学年高二下学期第一次月考数学试题(已下线)第五篇 向量与几何 专题4 极点与极线 微点3 极点与极线问题常见模型总结(一)
4 . 已知椭圆
的离心率为
,椭圆的上顶点为
,过点
且不垂直于x轴直线l与椭圆C相交于A、B两点.
(1)求椭圆C的方程;
(2)求
的取值范围;
(3)若点B关于x轴的对称点为点E,证明:直线AE与x轴相交于定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/310f780f4f03699023b1322a1e002539.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af74113f38fffeed8075e57d7f9d2533.png)
(1)求椭圆C的方程;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b0ba14e41e306e5633ad4bf1cdedd8.png)
(3)若点B关于x轴的对称点为点E,证明:直线AE与x轴相交于定点.
您最近一年使用:0次
2023-03-26更新
|
651次组卷
|
2卷引用:天津市第一百中学2022-2023学年高二下学期过程性诊断(1)数学试题
名校
解题方法
5 . 已知椭圆
的一个顶点为
,离心率为
.
(1)求椭圆的方程:
(2)过椭圆右焦点且斜率为
的直线
与椭圆相交于两点
,
轴交于点
,线段
的中点为
,直线
过点
且垂直于
(其中
为原点),证明直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bdfbae913ff7ff8caaefcaacf8c20ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆的方程:
(2)过椭圆右焦点且斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2799abb64fd7bfce9dfa7228aa460564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2022-07-07更新
|
1338次组卷
|
8卷引用:天津市部分区2021-2022学年高三上学期期末数学试题
天津市部分区2021-2022学年高三上学期期末数学试题四川省凉山州宁南中学2021-2022学年高二下学期第一次月考数学(文)试题江西省上饶市重点中学协作体2021-2022学年高二下学期期末联考数学(文)试题(已下线)专题27 椭圆(讲义)-2023年高考一轮复习精讲精练宝典(新高考专用)(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安徽省池州市青阳县第一中学2022-2023学年高二上学期11月期中考试数学试题宁夏六盘山高级中学2023届高三上学期期末考试数学(文)试题第三章 圆锥曲线的方程 讲核心03
2022·全国·模拟预测
解题方法
6 . 在平面直角坐标系
中,已知椭圆
的右焦点与抛物线
的焦点重合,且椭圆的四个顶点围成的四边形面积为
.
(1)求椭圆C的标准方程;
(2)已知点P是直线
上的动点,过点P作椭圆C的两条切线,切点分别为M,N,问直线MN是否过定点?若是,求出该定点;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/324b15493229b138185e692b3dd67814.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6093eebca8f3ff82ce9298feb197e955.png)
(1)求椭圆C的标准方程;
(2)已知点P是直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1611e005ab809ad6e282f4ff31d9cc5.png)
您最近一年使用:0次
7 . 已知椭圆
,且过
两点.
(1)求椭圆E的方程和离心率e;
(2)若经过
有两条直线
,它们的斜率互为倒数,
与椭圆E交于A,B两点,
与椭圆E交于C,D两点,P,Q分别是AB,CD的中点试探究:
与
的面积之比是否为定值?
若是,请求出此定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/284b0bbd9efab3e025e22684c13c5330.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44c5418050b7ad3ad5e66349c4a46fcb.png)
(1)求椭圆E的方程和离心率e;
(2)若经过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c9dcfd9f4c5298035870cb88a34169.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.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/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a9dabb53dc826019fc8b6ae6d940c5.png)
若是,请求出此定值;若不是,请说明理由.
您最近一年使用:0次
8 . 在平面直角坐标系xOy中,已知椭圆
,过右焦点
作两条互相垂直的弦AB,CD,设AB,CD中点分别为
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/19/dfa08e48-cb55-47bb-b099-3a594ef9ce33.png?resizew=189)
(1)写出椭圆右焦点
的坐标及该椭圆的离心率;
(2)证明:直线MN必过定点,并求出此定点坐标;
(3)若弦AB,CD的斜率均存在,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6be0b9fdd8005f371fcec6bc0844cff3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/19/dfa08e48-cb55-47bb-b099-3a594ef9ce33.png?resizew=189)
(1)写出椭圆右焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(2)证明:直线MN必过定点,并求出此定点坐标;
(3)若弦AB,CD的斜率均存在,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecfb02e157819a2bdd0f2790cbc825e9.png)
您最近一年使用:0次
名校
解题方法
9 . 已知椭圆
过点
,且
的焦距是椭圆
的焦距的3倍.
(1)求
的标准方程;
(2)设M,N是
上异于点P的两个动点,且
,试问直线
是否过定点?若过,求出定点坐标;若不过,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd486b8796b3454eab219c28ed131683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53679be20ae56723e1ecb77ebf0ebe59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afef4405c1756afae009f7ef9fd9196.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)设M,N是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f18fe75b94f62832d1a1ad44ed879a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
名校
解题方法
10 . 已知椭圆
的焦点为
,且
过点
.
(1)求
的方程;
(2)设
为椭圆
的右顶点,直线
与椭圆
交于
两点,且
均不是
的左、右顶点,
为
的中点.若
,试探究直线
是否过定点?若过定点,求出该定点坐标;若不过定点,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01db0118fedcf6fcdde99ee28fe5618a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dcc73856d3a8d8eed4a4bd06d8a961a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cb1e28556c619cf7ee2c9e24cea49e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2022-06-16更新
|
1292次组卷
|
6卷引用:湖北省2023届新高三摸底联考数学试题
湖北省2023届新高三摸底联考数学试题(已下线)知识点:直线与圆锥曲线关系 易错点3 恒成立意义不明导致定点问题错误江西省宜春市铜鼓中学2021-2022学年高二下学期期末质量检测数学(文)试题四川省泸县第一中学2023届高三二诊模拟考试数学(文)试题四川省绵阳南山中学2023届高三下学期4月绵阳三诊热身考试文科数学试题(已下线)第25讲 圆锥曲线直线圆过定点问题-【同步题型讲义】2022-2023学年高二数学同步教学题型讲义(人教A版2019选择性必修第一册)