题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135320-55840.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135320-31674.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135321-78015.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135321-52820.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135321-74653.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135320-31674.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135321-17072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135322-28484.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135322-41501.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135322-17918.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135322-44354.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135322-13188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135320-31674.png)
(2)设动点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135323-29706.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135323-50078.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135320-31674.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135323-84582.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135323-78161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135324-92830.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135324-62492.png)
解析
试题分析:本题主要考查椭圆的标准方程以及几何性质等基础知识,考查学生分析问题解决问题的能力和计算能力.第一问,由椭圆C过点(0,1)点,所以得到
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135324-92329.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135324-89330.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135325-66934.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135323-50078.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135325-80623.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135325-93127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135325-67061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135325-30377.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135326-41074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135326-47848.png)
试题解析:(1)由题意可知
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135326-11894.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135327-78707.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135327-54815.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135327-71800.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135327-54871.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135328-10655.png)
故椭圆的标准方程为:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135324-62492.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135328-93475.png)
∵M、N在椭圆上,∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135328-32887.png)
又直线OM与ON的斜率之积为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135323-78161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135328-53476.png)
于是
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135329-68128.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135329-39959.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135324-92830.png)
核心考点
试题【如图,已知点为椭圆右焦点,圆与椭圆的一个公共点为,且直线与圆相切于点.(1)求的值及椭圆的标准方程;(2)设动点满足,其中M、N是椭圆上的点,为原点,直线OM与】;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/20191023/20191023135307-55591.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135308-37175.jpg)
(1)求椭圆E的方程;
(2)在椭圆E上是否存点Q,使得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135308-17327.png)
(3)过椭圆E上异于其顶点的任一点P,作
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135308-21704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135308-90817.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135253-15619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135253-70658.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135253-23965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135254-74664.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135254-26825.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135254-67188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135254-86077.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135254-55471.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135254-26825.png)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135255-98752.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135254-86077.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135255-71571.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135255-34788.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135255-76047.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135240-35591.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135241-19554.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135241-36775.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135241-43450.png)
(1)求椭圆的方程;
(2)若C、D分别是椭圆长轴的左、右端点,动点M满足
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135241-62816.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135242-44072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135242-28641.png)
(3)在(2)的条件下,试问
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135242-43783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135222-28180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135222-62454.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135222-89355.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135223-16386.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135223-14039.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135222-28180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135223-16386.png)
(2)过点F的直线交抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135223-16386.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135223-25925.png)
(3)直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135223-52113.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135222-28180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135224-18646.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135224-25241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135222-28180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135208-25587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135208-80451.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135208-25587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135208-95190.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135208-10786.png)
(1)求椭圆的标准方程;
(2)设P为椭圆上一点,若过点M(2,0)的直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135209-20349.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135209-80677.png)
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