题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051158-74483.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051158-24106.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051158-18306.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051158-66757.gif)
(Ⅰ)若双曲线过点
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051159-74793.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051159-57779.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051159-63310.gif)
(Ⅱ)在(Ⅰ)的条件下,若
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051159-80145.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051200-33159.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051200-99574.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051200-68590.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051158-66757.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051200-19285.gif)
(Ⅱ)直线
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051200-68590.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051201-24994.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051201-58682.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051201-30731.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051201-99267.gif)
∴双曲线方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051202-74766.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051159-63310.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051202-38896.gif)
∴双曲线方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051200-19285.gif)
(Ⅱ)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051202-23391.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051158-66757.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051202-48028.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051202-62006.gif)
(1)当直线
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051200-68590.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051158-66757.gif)
(2)当直线
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051200-68590.gif)
可设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051200-68590.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051203-82739.gif)
∴直线
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051203-91675.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051203-85159.gif)
由①,②知
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051203-66878.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051203-24703.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051204-58054.gif)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051204-99145.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051204-83309.gif)
故直线
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051200-68590.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051201-24994.gif)
核心考点
试题【已知双曲线的离心率e=2,且、分别是双曲线虚轴的上、下端点 (Ⅰ)若双曲线过点(,),求双曲线的方程;(Ⅱ)在(Ⅰ)的条件下,若、是双曲线上不同的两点,且,求】;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/20191024/20191024051149-66888.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051150-67603.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051150-47718.gif)
(1)问点P在什么曲线上?并求出该曲线的方程;
(2)设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051150-90409.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051143-90919.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051144-74222.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051144-23731.gif)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051144-31141.gif)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051144-77554.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051145-11191.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051140-94516.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051140-16174.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051140-24357.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051140-72536.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051141-49133.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051141-69931.gif)
A.4a | B.2a | C.a | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051132-99724.gif)
(Ⅰ)求双曲线的标准方程;
(Ⅱ)求以双曲线的右准线为准线的抛物线的标准方程
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024051126-78533.gif)
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