名校
解题方法
1 . 椭圆
的左顶点为
,离心率为
.
(1)求椭圆
的方程;
(2)已知经过点
的直线
交椭圆
于
两点,
是直线
上一点.若四边形
为平行四边形,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c6162828793e697cb1ad643b287c4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)已知经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f56c293f834c993b5732c36359431eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a089c207e39a24d0d82aa853ac2bbb8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2022-05-12更新
|
2017次组卷
|
8卷引用:四川省宜宾市第四中学校2022-2023学年高二下学期开学考试数学(文)试题
名校
解题方法
2 . 已知O为坐标原点,椭圆
的离心率为
,且经过点
.
(1)求椭圆C的方程;
(2)直线l与椭圆C交于A,B两点,直线
的斜率为
,直线
的斜率为
,且
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e30f308f08426156c2229455aac75a4.png)
(1)求椭圆C的方程;
(2)直线l与椭圆C交于A,B两点,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02324abee955451054237a932230500a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7a2ef115b3e4d764e54e8b29e33b036.png)
您最近一年使用:0次
2022-04-24更新
|
575次组卷
|
6卷引用:四川省仁寿第一中学校南校区2023-2024学年高三上学期第一次调研考试文科数学试题
名校
解题方法
3 . 圆
的离心率为
,且过点
,点
分别为椭圆
的左顶点和右顶点.
(1)求椭圆
的标准方程;
(2)是否存在定点
,对任意过点
的直线
(
在椭圆
上且异于
两点),都有
.若存在,则求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef233ad3db01fa3ce9ee94eaad8e64e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)是否存在定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5abcf3ce160ae4879b8bd2f0c1ecea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.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/08a2d591f5b2eda9dc4e19da46830c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2022-03-03更新
|
712次组卷
|
5卷引用:四川省宜宾市第四中学校2022-2023学年高三下学期开学考试数学(理)试题
四川省宜宾市第四中学校2022-2023学年高三下学期开学考试数学(理)试题四川省宜宾市第四中学校2022-2023学年高三下学期开学考试数学(文)试题黑龙江省2021-2022学年高三下学期校际联合考试数学(理科)试题(已下线)专题30 圆锥曲线中的存在性问题- 2022届高考数学一模试题分类汇编(新高考卷)(已下线)第28讲 圆锥曲线存在性问题-【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)
名校
解题方法
4 . 如图,已知椭圆
,
,
分别是长轴的左、右两个端点,
是右焦点.椭圆
过点
,离心率为
.
(1)求椭圆
的方程;
(2)若直线
上有两个点
,
,且
.
①求
面积的最小值;
②连接
交椭圆
于另一点
(不同于点
),证明:
、
、
三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.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/8b8f9648c81481bb487a43f95c04d991.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/21/1235331f-ce13-48fa-bca6-dd45c9c17152.png?resizew=176)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.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/d1fdef703c3c483fe829f600dd6ee613.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5585a42c8f07ad90b94ace9db3d78994.png)
②连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe61d39d080872caa8973a70a3b4955.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/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
您最近一年使用:0次
2022-02-17更新
|
605次组卷
|
3卷引用:四川省遂宁市绿然学校2021-2022学年高三下学期开学考试理科数学试题
名校
解题方法
5 . 已知椭圆
的离心率为
,点
在椭圆
上,点
是
轴正半轴上的一点,过椭圆
的右焦点
和点
的直线
与椭圆
交于
两点.
(1)求椭圆
的标准方程;
(2)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af292f60c635d2bb4c38379c6bd04ac5.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/d053b14c8588eee2acbbe44fc37a6886.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/dad2a36927223bd70f426ba06aea4b45.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/7789a500686c7a73770404ead6af0590.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca07069001852295d67c5fb81925c292.png)
您最近一年使用:0次
2022-01-20更新
|
1032次组卷
|
4卷引用:四川省成都市树德中学2023-2024学年高二下学期入学考试数学试卷
名校
解题方法
6 . 已知椭圆
的离心率
,直线
被以椭圆C的短轴为直径的圆截得的弦长为
.
(1)求椭圆C的方程.
(2)过点M(4,0)的直线交椭圆于A,B两个不同的点,问:是否存在实数
,使得
,若存在,求出
的范围,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de85df85401e7e8da683ea4a784963c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7347b88954b4a322f82c38a6af61e5c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求椭圆C的方程.
(2)过点M(4,0)的直线交椭圆于A,B两个不同的点,问:是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54c3b8df5c8bdb1002c3c8ecd41df38c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
解题方法
7 . 已知
是椭圆
的两个焦点,
为
上一点,
为坐标原点.
(1)若△
是等边三角形,求
的离心率;
(2)如果存在点
,使得
,且△
的面积等于
,求
的值和
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef6b94e42869013745050aba059b58dd.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/1dde8112e8eb968fd042418dd632759e.png)
(1)若△
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4d843550110289122b68cbdb1eddfbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)如果存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2427943a38dcd93c9ec9b735ffc9fe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf8a7029669bf1774a24f3ef6273ca88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/814397354c2ae1cb08e0271305970811.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2021-03-22更新
|
166次组卷
|
2卷引用:四川省成都市蓉城名校联盟2020~2021学年下学期入学联考高二文科数学试题
名校
解题方法
8 . 已知椭圆
的离心率为
,点
在椭圆上.
(1)求椭圆C的方程;
(2)设椭圆的左右顶点分别是A、B,过点
的动直线与椭圆交于M,N两点,连接
、
相交于G点,试求点G的横坐标的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db81446766bb8f493d6fc49e65f0d495.png)
(1)求椭圆C的方程;
(2)设椭圆的左右顶点分别是A、B,过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f579b73ca01978ec68e716f993bc3766.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
您最近一年使用:0次
2021-03-10更新
|
296次组卷
|
2卷引用:四川省绵阳市南山中学2020-2021学年高二下学期开学考试数学(文)试题
名校
9 . 已知椭圆
的离心率为
,椭圆的中心
到直线
的距离为
.
(1)求椭圆
的方程;
(2)设过椭圆
的右焦点
且倾斜角为
的直线
和椭圆交于
两点,对于椭圆
上任意一点
,若
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dccdc4f73b409dae07a0661a4281ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa82a15632a545ce2cc6dc998899807.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设过椭圆
![](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/30c20e88a33043f4279fff360c81006e.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99dfd10c7047fad7f794684179eaf357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1adebff9fb726cd58eda1ef994890901.png)
您最近一年使用:0次
2020-12-16更新
|
715次组卷
|
5卷引用:四川省遂宁市绿然学校2022-2023学年高三上学期入学考试数学理科试题
名校
解题方法
10 . 已知椭圆C:
+
=1(a>b>0)的离心率为
,且经过点P
,左、右焦点分别为F1,F2.
(1)求椭圆C的方程;
(2)过F1的直线l与椭圆C相交于A,B两点,若△AF2B的内切圆半径为
,求以F2为圆心且与直线l相切的圆的方程.
![](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/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2de52259b426acb42761fec59a7748.png)
(1)求椭圆C的方程;
(2)过F1的直线l与椭圆C相交于A,B两点,若△AF2B的内切圆半径为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dddd9f54eebb015ca343e7ae075b53cf.png)
您最近一年使用:0次