解题方法
1 . 已知
的离心率为
,短轴长为2,F为右焦点.
(1)求椭圆的方程;
(2)在x轴上是否存在一点M,使得过F的任意一条直线l与椭圆的两个交点A,B,恒有
,若存在求出M的坐标,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
(1)求椭圆的方程;
(2)在x轴上是否存在一点M,使得过F的任意一条直线l与椭圆的两个交点A,B,恒有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e57610afd116ab84660c807cc1aa3819.png)
您最近一年使用:0次
2022高三·全国·专题练习
名校
解题方法
2 . 已知椭圆
过点
,且离心率
为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eff998d034284391ca064755fa6bf1b.png)
(1)求椭圆
的方程;
(2)
、
是椭圆上的两个动点,如果直线
的斜率与
的斜率互为相反数,证明直线
的斜率为定值,并求出这个定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dae13b2a96f91ab64fb4948de2b0ae10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24261b8fc52ec9a02831a4742c0ba6fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eff998d034284391ca064755fa6bf1b.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ff575e55857af133edb24c8e61504f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0215e13a9fb5574d5194aeb9507a98aa.png)
您最近一年使用:0次
3 . 已知椭圆
的左右焦点分别为
,
,其离心率为
,P为椭圆C上一动点,
面积的最大值为
.
(1)求椭圆C的方程;
(2)过右焦点
的直线l与椭圆C交于A,B两点,试问:在x轴上是否存在定点Q,使得
为定值?若存在,求出点Q的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.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/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002ed1ebb2cb936e10ab478789f91c7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求椭圆C的方程;
(2)过右焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8d24822b6415ac090b31fe5010641cf.png)
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2022-01-08更新
|
1358次组卷
|
5卷引用:浙江省绍兴市第一中学2021-2022学年高三上学期期末数学试题
浙江省绍兴市第一中学2021-2022学年高三上学期期末数学试题湖南省益阳市第一中学2022届高三上学期第四次月考数学试题(已下线)专题14 解析几何中的范围、最值和探索性问题(讲)--第一篇 热点、难点突破篇-《2022年高考数学二轮复习讲练测(新高考·全国卷)》内蒙古包钢第一中学2022届高三一模数学(文)试题安徽省桐城中学2021-2022学年高二下学期开学检测数学试卷
解题方法
4 . 已知椭圆
的离心率为
且经过点
.
(1)求椭圆方程;
(2)直线
交椭圆于不同两点
,若
,
(
是坐标原点)的面积等于
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe8530b8e246a9a5ec9fe3b9c347d5a.png)
(1)求椭圆方程;
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b256345d7109e081b7c895591e995d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19efd2f2662ca444c784b69e35f53120.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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5 . 1.已知椭圆
的离心率为
,过焦点且垂直于长轴的弦长等于1
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/19/cc9b7092-8503-4945-b975-70144fe62f71.png?resizew=284)
(1)求椭圆的方程;
(2)直线
交椭圆于A,B两点,且AB被直线
平分.
①若
的面积等于1(O是坐标原点),求l的方程;
②椭圆的左右焦点分别是
,
,
,
的重心分别是
,
,当原点O落在以CD为直径的圆外部时,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/19/cc9b7092-8503-4945-b975-70144fe62f71.png?resizew=284)
(1)求椭圆的方程;
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f24e616b5a35ff372c78c1472f156ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f52cb58b6bc5d71030463ba7e28134.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
②椭圆的左右焦点分别是
![](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/d3c07ebcbfacda073208d483c58e8a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5eb2485f90dbfd0dfd6e7d179a856f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
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2021-11-04更新
|
1255次组卷
|
3卷引用:浙江省绍兴市诸暨市2017-2018学年高二上学期期末数学试题
6 . 如图,椭圆
的离心率为
且经过点
,
为椭圆上的一动点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/682b1279-5925-488f-b2e8-6d917d4686a6.png?resizew=164)
(1)求椭圆
的方程;
(2)设圆
,过点
作圆
的两条切线
,
,两切线的斜率分别为
,
.
①求
的值;
②若
与椭圆
交于
,
两点,与圆
切于点
,与
轴正半轴交于点
,且满足
,求
的方程.
![](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/3ef233ad3db01fa3ce9ee94eaad8e64e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/682b1279-5925-488f-b2e8-6d917d4686a6.png?resizew=164)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc64ba34f941b2ac154f8d7bc99f915d.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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4757181824e15e0f21e5bdd55448783.png)
②若
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6869cf71c3849484d7d6530b16431185.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
您最近一年使用:0次
名校
7 . 已知F是椭圆
的左焦点,A是该椭圆的右顶点,过点F的直线l(不与x轴重合)与该椭圆相交于点M,N.记
,设该椭圆的离心率为e,下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b24214f111f7c6d2b64e53ad970438b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b5e653928a34270ea33155670ef412e.png)
A.当![]() ![]() | B.当![]() ![]() |
C.当![]() ![]() | D.当![]() ![]() |
您最近一年使用:0次
2021-05-12更新
|
2378次组卷
|
13卷引用:浙江省杭州第九中学2021-2022学年高二上学期期末数学试题
浙江省杭州第九中学2021-2022学年高二上学期期末数学试题(已下线)2021年秋季高三数学开学摸底考试卷01(浙江专用)(已下线)高二上学期期末【全真模拟卷01】-2022-2023学年高二数学考试满分全攻略(人教A版2019选修第一册)四川省达州市2021 届高三二模数学(理)试题(已下线)考点突破13 圆锥曲线的方程-备战2022年高考数学一轮复习培优提升精炼(新高考地区专用)四川省成都市第七中学2021-2022学年高三上学期入学考试理科数学试题安徽师范大学附属中学2021-2022学年高三上学期入学考试理科数学试题(已下线)第01讲 椭圆-【帮课堂】2021-2022学年高二数学同步精品讲义(苏教版2019选择性必修第一册)(已下线)3.1 椭圆的几何性质-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册) (已下线)卷09 高二上学期12月阶段测-【重难点突破】2021-2022学年高二数学上册常考题专练(人教A版2019选择性必修第一册)(已下线)专题25 圆锥曲线压轴小题必刷100题-【千题百练】2022年新高考数学高频考点+题型专项千题百练(新高考适用)四川省成都市第七中学2021-2022学年高三上学期入学考试理科数学试题(已下线)专题19 圆锥曲线(讲义)-2
19-20高一·浙江杭州·期末
8 . 已知椭圆
,
的离心率为
,且过点
.
![](https://img.xkw.com/dksih/QBM/2020/11/8/2588698550009856/2588725925707776/STEM/4aafa3606f9f4e91982c67a9e3158a21.png?resizew=174)
(1)求椭圆C的标准方程;
(2)设椭圆C的左、右顶点分别为A、B,M、N是椭圆C上异于A、B的两点,直线
,
交于点
,记
的面积分别是
,
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d72a07a4e5acfc140a3cea1f26b951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f82eb4ba631d0f50d848aa6e576b379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2de52259b426acb42761fec59a7748.png)
![](https://img.xkw.com/dksih/QBM/2020/11/8/2588698550009856/2588725925707776/STEM/4aafa3606f9f4e91982c67a9e3158a21.png?resizew=174)
(1)求椭圆C的标准方程;
(2)设椭圆C的左、右顶点分别为A、B,M、N是椭圆C上异于A、B的两点,直线
![](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/3129f8b74b3e828a19d1ec4a017ceeb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5deeddf8b194c4d6a460f3b9ea84a8dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7cebeed3115451ddd76786091e3d247.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d11838fc8ecb05bb9a7bd2c94e2511.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13e21e2c5ca9a1ec2d8ce9d05134a6c0.png)
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名校
解题方法
9 . 已知点F是椭圆
的上焦点,点P在椭圆E上,线段PF与圆
相切于点Q,O为坐标原点,且
,则椭圆E的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fb223b8777ab973970491bf0dcc6806.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75a31a04a490da32b9b05486981c15b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c9c3422d623920b75d2fdad04a975ed.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2020-07-16更新
|
1349次组卷
|
2卷引用:浙江省浙南名校联盟2019-2020学年高二下学期期末联考数学试题
解题方法
10 . 过原点的一条直线与椭圆
交于A,B两点,
为椭圆右焦点,且AB长度等于焦距长,若
,则该椭圆离心率的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/056366603f9609952b4ff765cfd88911.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次