解题方法
1 . 已知椭圆的两焦点分别为
和
,短轴的一个端点为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45c8951cfef9a9a426f51f980395f6f0.png)
(1)求椭圆的标准方程;
(2)椭圆上是否存在一点
使得
?若存在求
的面积,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acfbefa33aea2f969cde55b15d7f8454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03f33f5a4eaaf9360893edfd15e7dd97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45c8951cfef9a9a426f51f980395f6f0.png)
(1)求椭圆的标准方程;
(2)椭圆上是否存在一点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc5c19ac440746be97d8b46af5d288a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da0bd0c0d318cc6cb8e2a1c56c463f19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb643c6a6a0f51f7ec36ddc48c9d3184.png)
您最近一年使用:0次
2022-10-22更新
|
1081次组卷
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2卷引用:新疆维吾尔自治区喀什地区喀什十四校2023-2024学年高二上学期期末数学试题
解题方法
2 . 如图,已知椭圆
的左、右焦点分别为
,
,直线
经过
与桶圆
交于
,
两点,且
的周长为12.
![](https://img.xkw.com/dksih/QBM/2020/12/27/2623177665970176/2625280923459584/STEM/47248ec3-6f1d-4d07-b31c-f2994214f5a1.png)
(1)求椭圆
的离心率.
(2)若
,
分别为椭圆的左、右顶点,记直线
,
的斜率分别为
,
,证明:
是定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b35a77ce2b5d66c76b336a48d9d3340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f491706aa7497d2f2a5056b225d3f056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/e5eb2485f90dbfd0dfd6e7d179a856f5.png)
![](https://img.xkw.com/dksih/QBM/2020/12/27/2623177665970176/2625280923459584/STEM/47248ec3-6f1d-4d07-b31c-f2994214f5a1.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](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/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6f62ec9c0e58b3f1c363158269b14d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ff131c92aa9e10f696d374216cdcf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2562b7eff060212ab6fa86606571641.png)
您最近一年使用:0次
2020-12-30更新
|
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3卷引用: 新疆和田地区皮山县高级中学2023-2024学年高二上学期1月期末数学试题
名校
3 . 已知椭圆C:
=1(a>b>0)的离心率为
,其内接正方形的面积为4.
(Ⅰ)求椭圆C的标准方程;
(Ⅱ)设M为椭圆C的右顶点,过点
且斜率不为0的直线l与椭圆C相交于P,Q两点,记直线PM,QM的斜率分别为k1,k2,求证:k1k2为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2aa6ee9b173abc2191c1c19c5392ff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f78c38805c09dcfbcc42103308975a74.png)
(Ⅰ)求椭圆C的标准方程;
(Ⅱ)设M为椭圆C的右顶点,过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1dc3354ff37472e07900f0d36fa2dc8.png)
您最近一年使用:0次
2019-04-26更新
|
1958次组卷
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2卷引用:新疆乌苏市第一中学2020-2021学年高二(4-27班)下学期入学检测数学试题