题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154017-67514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154017-84403.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154017-69910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154017-72129.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154018-40401.png)
(2)设过点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154018-41499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154018-54096.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154018-10012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154018-82168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154018-10012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154019-95865.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154019-73799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154019-45789.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154018-54096.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154019-42478.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154020-96716.png)
解析
试题分析:(1)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154020-51099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154020-38397.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154020-94666.png)
设椭圆方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154020-75648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154017-69910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154021-60191.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154021-92036.png)
所以椭圆方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154019-42478.png)
(2)易知直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154018-54096.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154018-54096.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154021-47319.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154021-49785.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154022-99194.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154022-14820.png)
由题意知
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154022-95292.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154022-31282.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154023-44475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154023-44267.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154023-48615.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154023-43798.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154019-73799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154019-45789.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154023-88431.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154024-16129.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154024-28202.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154024-58342.png)
将
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154024-78259.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154024-58604.png)
将④代入⑤
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154025-89842.png)
整理化简得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154025-32355.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154025-58616.png)
所以直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154018-54096.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154020-96716.png)
点评:本题考查了椭圆方程的求法,以及直线与椭圆的综合应用,为圆锥曲线的常规题,应当掌握。考查了学生综合分析问题、解决问题的能力,知识的迁移能力以及运算能力。解题时要认真审题,仔细分析。
核心考点
试题【已知椭圆的离心率为,且过点,为其右焦点.(1)求椭圆的方程; (2)设过点的直线与椭圆相交于、两点(点在两点之间),若与的面积相等,试求直线的方程.】;主要考察你对椭圆的定义与方程等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154006-88278.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154006-39942.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154006-96195.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154006-39163.png)
(2)是否存在过点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154006-81059.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154007-23642.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154007-19843.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154007-23642.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153956-16712.png)
A. 10 | B. 5 | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153949-95073.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153942-48955.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153942-84539.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153943-43816.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153943-65021.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153943-12485.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153943-26117.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153943-26117.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153942-48955.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153932-86230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153932-21547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153932-58194.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153933-67293.png)
(1)求曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153932-86230.png)
(2)设过(0,-2)的直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153933-30722.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153932-86230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153933-50884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153933-51117.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153933-27447.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153933-30722.png)
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