解题方法
1 . 已知椭圆
的右焦点为
,且经过点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1a05549fb72d4f490f2d658e2b1812.png)
(1)求椭圆C的标准方程:
(2)经过椭圆C的右焦点作倾斜角为
的直线l,直线l与椭圆相交于M,N两点,求线段MN的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3324199c6751f2e0e6d8542783b0d957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f363d815fde5c34c317df8c6a1d616.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1a05549fb72d4f490f2d658e2b1812.png)
(1)求椭圆C的标准方程:
(2)经过椭圆C的右焦点作倾斜角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b342d5cb6dd1c84a82f6aca68ed829c.png)
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解题方法
2 . 已知椭圆
:
(
)的离心率为
,点
是
上一点,
,
分別是两个焦点,则
的面积为( )
![](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/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff7f12ef3d9b10299421cb66327293ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/b42fc33bcfc63ec2f4940ccd3f862400.png)
A.![]() | B.![]() | C.16 | D.32 |
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3 . 已知
在椭圆
上,
分别为
的左、右焦点.
(1)求椭圆
的离心率;
(2)若动点
均在
上,且
在
轴的两侧,求四边形
的周长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/246668e713de36a9e3af9b0d0d3ee9e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/f6bce3d91ca23b86d8c6625f2632e437.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2bb9c075a320b0fe23145061b1fb0f8.png)
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解题方法
4 . 根据下列条件,分别求出曲线的标准方程:
(1)焦距是
,过点
,焦点在
轴上的椭圆;
(2)一个焦点是
,一条渐近线方程为
的双曲线;
(3)焦点到准线的距离是
,而且焦点在
轴上的抛物线.
(1)焦距是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b273241821170be56c5251d48386013b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(2)一个焦点是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c3eda23a1350120ef959ae541d36657.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/953b0e963195605a67975c6f8f3caa0c.png)
(3)焦点到准线的距离是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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解题方法
5 . 已知椭圆
的右焦点为
,且过点
.
(1)求C的方程;
(2)若过点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
的直线与
交于
两点,
为坐标原点,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce176fdfbb44b8459f441a8d805013f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef233ad3db01fa3ce9ee94eaad8e64e.png)
(1)求C的方程;
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9da30f3b77f2318f2000fa009979f04c.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
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名校
解题方法
6 . 求适合下列条件的椭圆的标准方程:
(1)两个焦点的坐标分别是
,椭圆上一点P到两焦点距离的和是10;
(2)焦点在y轴上,且经过两个点
和
;
(3)经过
和点
.
(1)两个焦点的坐标分别是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32913a9e8f6ad754d6434c0549ba4fde.png)
(2)焦点在y轴上,且经过两个点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b094cba781181aeb90752170e9ba6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
(3)经过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fd2419c1641f1a7dc043a0a264ac483.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b8bbc1781630588ea1f58f693b8893b.png)
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名校
7 . 已知㭻圆
:
(
)经过点
,离心率为
.
(1)求椭圆
的方程;
(2)直线
与椭圆
交于点
(异于顶点)与
轴交于点
,点
为椭圆的右焦点,
为坐标原点,
,求直线
的方程.
![](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/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f9d386c75aa97e31c5fb37e047bc336.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
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2024-01-19更新
|
570次组卷
|
2卷引用:天津市四校2023-2024学年高二上学期期末联考数学试卷
名校
解题方法
8 . 焦点在
轴上的椭圆过点
,且点
到两焦点的距离之和为8,则该椭圆标准方程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2b337c32bd5408c0ed8a9ee9cde4cad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
名校
解题方法
9 . 已知椭圆
,
四个点中恰有三个点在椭圆C上,则椭圆C的方程是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/323227dd8a7a31c078eac609b9acf472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a0b6b1ffeaf7509c0f5ac1d9777744c.png)
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2024-01-14更新
|
178次组卷
|
7卷引用:天津市和平区耀华中学2019-2020学年高二上学期期末数学试题
天津市和平区耀华中学2019-2020学年高二上学期期末数学试题上海市松江一中2022-2023学年高二下学期期末数学试题(已下线)期末真题必刷基础60题(31个考点专练)【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一、二册)(已下线)上海市高二下学期期末真题必刷02(基础题)--高二期末考点大串讲(沪教版2020选修)(已下线)上海市静安区2023届高三二模数学试题变式题1-5陕西省渭南市富平县2024届高三上学期摸底考试理科数学试题(已下线)2.2.1 椭圆的标准方程(十三大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
解题方法
10 . 设椭圆
经过点
,且其左焦点坐标为
.
(1)求椭圆的方程;
(2)对角线互相垂直的四边形
的四个顶点都在
上,且两条对角线均过
的右焦点,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac5b4d0583e8b68caf2125d0b4ce6a2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2a5e336b6bcba6354fd366c892dd06.png)
(1)求椭圆的方程;
(2)对角线互相垂直的四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c761dad84bd29109dc0ffc31b9cbbd46.png)
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