题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224140-62617.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224140-60192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224141-33415.png)
(1)求证:KF平分∠MKN;
(2)O为坐标原点,直线MO、NO分别交准线于点P、Q,求
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224141-55219.png)
答案
解析
试题分析:(1)只需证
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224141-81416.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224141-82955.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224141-55219.png)
试题解析:(1)抛物线焦点坐标为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224141-75879.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224142-92556.png)
设直线MN的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224142-35240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224142-27565.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224142-21434.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224143-72488.png)
设KM和KN的斜率分别为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224143-14698.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224143-27718.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224143-29838.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224144-80300.png)
(2)设M、N的坐标分别为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224142-27565.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224144-25344.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224144-61964.png)
设直线MN的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224142-35240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224142-21434.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224144-69279.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224144-91792.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224145-25879.png)
又直线MN的倾斜角为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224145-27088.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224145-39677.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224145-31129.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224145-98196.png)
同理可得
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224146-21245.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224146-27235.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224146-69615.png)
核心考点
试题【如图,已知抛物线的焦点为F,过F的直线交抛物线于M、N两点,其准线与x轴交于K点.(1)求证:KF平分∠MKN;(2)O为坐标原点,直线MO、NO分别交准线于点】;主要考察你对曲线与方程的应用等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224126-32148.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224126-13913.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224126-97206.png)
轴垂直,椭圆的离心率
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224126-41674.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224126-60058.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224127-75744.jpg)
(1)求此椭圆的标准方程;
(2)设P是此椭圆上异于A,B的任意一点,
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224127-76790.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224126-13913.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224127-31759.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224127-69008.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224128-61596.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224128-92364.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224128-33377.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224105-66760.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224106-57309.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224106-69318.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224106-67560.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224106-51164.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224106-70567.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224107-42749.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224107-19335.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224107-68323.png)
(Ⅰ)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224106-70567.png)
(Ⅱ)如图,动直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224107-65563.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224106-70567.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224108-57233.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224108-90401.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224108-11895.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224108-93596.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224109-54126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224109-49508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224110-88366.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224056-59242.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224056-54122.png)
(1)若点C坐标为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224056-99874.png)
(2)过点P(m,0)作倾角为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224057-83899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224057-92538.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224043-31863.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224043-14464.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224043-56521.png)
(Ⅰ)求椭圆的方程;
(Ⅱ)求m的取值范围;
(Ⅲ)若直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224043-80207.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224037-53263.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224037-82043.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224038-59611.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224038-65143.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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