名校
解题方法
1 . 已知椭圆
的焦点在x轴上,满足短轴长等于焦距,且长轴两端点与上顶点构成的三角形面积为
.
(1)求椭圆
的标准方程及离心率;
(2)若双曲线
与(1)中椭圆
有相同的焦点,且过点
,求双曲线
的标准方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bbda5be680a2c8bfa775e2a87f192e7.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)若双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf95879032efacfbdeb85b1f9f656874.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
您最近一年使用:0次
2021-02-03更新
|
660次组卷
|
6卷引用:吉林省长春市农安县五校联考2020-2021学年高二上学期期末考试数学(文)A卷试题
2 . 如图,已知椭圆
左、右焦点分别为
,
,右顶点为
,上顶点为
,
为椭圆上在第一象限内一点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/6057b130-80a7-4e99-ab73-699012e5954d.png?resizew=192)
(1)若
,求椭圆的离心率;
(2)若
,求直线
的斜率
;
(3)若
、
、
成等差数列,椭圆的离心率
,求直线
的斜率
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/6057b130-80a7-4e99-ab73-699012e5954d.png?resizew=192)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c0956d6e0406140a2736d82db342d2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d3e81540f1f8e505955955b1a45c13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85e2e2c0bc5a39489af0506151ad55f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/619c60578ea4627a20c0b13c9b316ad3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f846125f221875283391a0d9bb00d99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b06233d6841870f39860207d110d7271.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2021-01-29更新
|
527次组卷
|
2卷引用:江苏省镇江市第一中学2020-2021学年高二上学期期末数学试题
3 . 已知点F是椭圆
的右焦点,P是椭圆E的上顶点,O为坐标原点且
.
(1)求椭圆的离心率e;
(2)已知
,
,过点M作任意直线l与椭圆E交于A,B两点.设直线
,
的斜率分别为
,
,若
,求椭圆E的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13d9eefe139c944217b87db7c06191b6.png)
(1)求椭圆的离心率e;
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a29ba49963134a7232fa8574105fc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/354b980819c6ba892ce0e9ecead90634.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ec7bcf5820dfe70290259c2d7ac1ea5.png)
您最近一年使用:0次
2021-01-19更新
|
1384次组卷
|
5卷引用:安徽省淮北市2021届高三一模数学(文)试题
安徽省淮北市2021届高三一模数学(文)试题(已下线)专题10 解析几何(测)-2021年高考数学二轮复习讲练测(新高考版)(已下线)专题10 解析几何(测)-2021年高考数学二轮复习讲练测(文理通用)广东省广州英豪学校2020-2021学年高二下学期开学检测数学试题(已下线)专题7-4圆锥曲线五个方程型大题归类-1
名校
解题方法
4 . 在平面直角坐标系
中,已知圆
,椭圆
,
为椭圆的右顶点,过原点
且异于坐标轴的直线与椭圆
交于
两点,直线
与圆
的另一个交点为
,直线
与圆
的另一个交为
,设直线
的斜率分别为
,
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/b04d5596-2849-4cb7-8008-351c313a01a1.png?resizew=200)
(1)求椭圆的离心率;
(2)求
的值;
(3)求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7795aec93c2c7ac2fd93e6747ca6516c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a61f89c4a7e5d264bba22794a9a1403c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc7da8ae0b0b96535db96d4f1a07243b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/b04d5596-2849-4cb7-8008-351c313a01a1.png?resizew=200)
(1)求椭圆的离心率;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4757181824e15e0f21e5bdd55448783.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8bba9be15b2def55c1dd9d54d0629b5.png)
您最近一年使用:0次
2021-08-26更新
|
488次组卷
|
2卷引用:浙江省嘉兴市第五高级中学2018-2019学年高二下学期期中数学试题
解题方法
5 . 已知点
和椭圆
.
(1)设椭圆的两个焦点分别为
,试求
的周长及椭圆的离心率;
(2)若直线
与椭圆
交于两个不同的点
,设直线
与
的斜率分别为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677b1e953bfbedbc5e390e87c5a1be71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69daca955a565fa537347dd0d93783f.png)
(1)设椭圆的两个焦点分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f731b9b32af52fa59ac34047e900fc67.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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83d200a411fbc2f50ad72f1fd729a7d7.png)
您最近一年使用:0次
2022-04-24更新
|
309次组卷
|
2卷引用:天津市红桥区2016-2017学年高三上学期期末理科数学试题
解题方法
6 . 椭圆的标准方程
.求长轴长、短轴长、焦距焦点坐标、顶点坐标以及离心率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1205114787722e9cc9511c485cbd5d40.png)
您最近一年使用:0次
名校
7 . 已知椭圆
经过点
.
(1)求椭圆
的方程及其离心率;
(2)过椭圆右焦点
的直线(不经过点
)与椭圆交于
、
两点,当
的平分线为
时,求直线
的斜率
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a5b087c270dfc3f5ac18ebbc07edf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfc2210a7e09298897f6585ad08a70d3.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过椭圆右焦点
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb686e4f5e3938575bc547e849d5513f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2021-01-13更新
|
88次组卷
|
2卷引用:陕西省西安市长安区第一中学2019-2020学年高二下学期第一次质量检测数学(文)试题
解题方法
8 . 已知双曲线与椭圆
有相同焦点,且经过点
.
(1)求焦点坐标及椭圆的离心率;
(2)求此双曲线的标准方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9f61d2f4f9bfe2a934c7cc5ff9778af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f1f4c01d598b757fb8f7b384794bd18.png)
(1)求焦点坐标及椭圆的离心率;
(2)求此双曲线的标准方程.
您最近一年使用:0次
2021-01-09更新
|
376次组卷
|
4卷引用:甘肃省甘南藏族自治州卓尼县第一中学2019-2020学年高二下学期期末数学理科试题
名校
9 . 已知椭圆E:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f84c3d766b73ed66f258b6a99cdaf57.png)
,圆C:x2+y2=r2.
(1)若椭圆的离心率为
,且长轴长为18,求椭圆的标准方程;
(2)若椭圆E上任意一点不在圆C外部,求椭圆离心率的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f84c3d766b73ed66f258b6a99cdaf57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0608ee781f51ad22cb551009c811d142.png)
(1)若椭圆的离心率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe2c533dbc23a34518f72f3cb14f330.png)
(2)若椭圆E上任意一点不在圆C外部,求椭圆离心率的取值范围.
您最近一年使用:0次
名校
解题方法
10 .
,
分别是椭圆C:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
的左,右焦点,过
作直线交椭圆C于上顶点A,与椭圆C的另一个交点为B,且
.
(1)求椭圆C的离心率;
(2)已知
的面积为
,求椭圆
的方程.
![](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/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f82eb4ba631d0f50d848aa6e576b379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74064c3fa84f604f6636f6bbf778bdc1.png)
(1)求椭圆C的离心率;
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29bf0cf2f9b056030f17dfba06f62b1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c69e14c265da152d1350dce6772509aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次