题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040420-24742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040420-30282.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040420-98328.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040420-98328.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040420-67588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040420-89496.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040420-12513.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040420-98328.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040420-45435.png)
(1)求曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040420-98328.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040420-70611.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040420-98328.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040420-75456.png)
(3)若以
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040421-50521.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040421-86882.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040421-50521.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040421-79051.png)
(2)由双曲线的对称性知,不妨设P在左支上,设
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040421-75079.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040421-63445.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040421-50764.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040421-31422.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040422-21761.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040422-59677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040420-75456.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040422-83230.png)
(3)设
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040422-26787.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040422-89731.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040422-56009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040422-17561.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040422-90512.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040423-19304.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040423-56860.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040423-42567.png)
代入的
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040423-43499.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040423-23716.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040423-32454.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040423-61461.png)
即得PQ过定点
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040424-38459.png)
(说明:另解一,可以利用对称和当PQ垂直情况猜过
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040424-52737.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040424-38459.png)
另解二,设AP斜率,求出P,Q坐标,然后利用两点式写出方程判断过定点
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040424-38459.png)
解析
核心考点
试题【已知双曲线,点在曲线上,曲线的离心率为,点、为曲线上易于点A的任意两点,为坐标原点。(1)求曲线上方程;(2)若为曲线的焦点,求最大值;(3)若以为直径的圆过点】;主要考察你对双曲线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/20191024/20191024040405-86516.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040405-32180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040406-58194.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040406-68052.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040406-62956.png)
(1)求双曲线的方程;
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040406-79400.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040407-79038.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040407-84362.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040407-72651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040407-20921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040408-21076.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040408-81188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040358-28147.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040358-76122.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040358-84012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040359-25642.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040351-95930.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040351-76254.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040339-47053.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040340-10023.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040340-87288.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040340-55343.png)
A.24 | B.25 | C.4 | D.7 |
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024040329-24332.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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