题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153717-96398.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153717-42400.png)
上顶点为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153717-60948.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153717-76176.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153717-81151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153718-67828.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153718-95335.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153718-26112.png)
(Ⅰ)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153718-25579.png)
(Ⅱ)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153718-60635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153718-91677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153718-60635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153718-76632.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153718-25579.png)
(Ⅲ)在(Ⅱ)的条件下,过右焦点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153718-11039.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153719-88228.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153719-99241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153718-25579.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153719-91032.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153719-75726.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153717-76176.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153720-25184.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153720-92235.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153720-13177.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153720-25099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153720-70166.png)
解析
试题分析:解:(Ⅰ)连接
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153721-88222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153718-95335.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153721-90813.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153721-25311.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153721-78885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153720-13177.png)
(Ⅱ)由(1)知
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153721-44944.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153721-30469.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153721-78289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153722-13745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153722-56166.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153722-74687.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153722-46145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153718-60635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153718-76632.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153723-17114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153723-50863.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153723-27297.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153723-74942.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153720-25099.png)
(Ⅲ)由(Ⅱ)知
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153723-46199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153723-43410.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153724-90521.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153724-96834.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153724-35087.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153724-67154.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153725-97874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153725-23315.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153725-66395.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153725-88907.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153725-89041.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153725-81580.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153726-81143.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153719-75726.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153726-92219.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153726-96679.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153719-75726.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153726-51310.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153726-80441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153719-75726.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153726-87493.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153727-66622.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153727-59327.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153727-32437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153727-87091.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153727-37616.png)
综上可知实数
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153720-92235.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153720-70166.png)
点评:关于曲线的大题,难度相对都较大。对于题目涉及到关于直线和其他曲线的交点时,一般都可以用到跟与系数的关系式:在一元二次方程
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153727-36183.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153727-43257.png)
核心考点
试题【设椭圆的左、右焦点分别为,上顶点为,在轴负半轴上有一点,满足,且.(Ⅰ)求椭圆的离心率;(Ⅱ)是过三点的圆上的点,到直线的最大距离等于椭圆长轴的长,求椭圆的方程】;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/20191023/20191023153652-49682.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153652-58332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153652-20979.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153652-78103.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153652-20738.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153653-81103.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153653-69231.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153653-84756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153653-71225.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153654-51626.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153654-12744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153654-74405.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153654-40069.png)
(1)求椭圆的方程;
(2)是否存在定点M、N,使得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153655-99562.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153647-87222.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153627-75714.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153627-55145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153628-90662.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153623-19844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153623-11951.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153617-66216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153617-20771.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153617-14136.png)
(1)求e的值;
(2)试判定原点关于l的对称点是否在椭圆上,并说明理由。
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