题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034206-13699.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034206-63191.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034206-70807.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034206-37868.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034206-73641.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034206-70954.png)
(Ⅰ)求曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034206-78048.png)
(Ⅱ)求AB的直线方程;
(Ⅲ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034206-64064.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034207-37733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034207-28941.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034207-71457.png)
解析
(1)根据双曲线的定义可以得到双曲线的方程的求解。
(2)联立方程组,得到相交弦的长度以及韦达定理得到直线的方程。
(3)根据
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034207-78019.png)
解:(Ⅰ)由双曲线的定义可知,曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034206-78048.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034207-72227.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034207-76060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034207-58435.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034207-74015.png)
故曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034206-78048.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034207-37733.png)
(Ⅱ) 设
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034207-53216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034208-54184.png)
消去
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034208-43228.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034208-76402.png)
又已知直线与双曲线左支交于两点
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034208-98936.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034208-53098.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034208-86053.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034208-75661.png)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034208-59853.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034208-70926.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034209-64873.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034209-25966.png)
依题意得
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034209-52866.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034209-41970.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034209-36872.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034209-56566.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034208-86053.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034210-95161.png)
故直线
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034210-97680.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034207-28941.png)
(Ⅲ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034210-84434.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034207-78019.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034210-68803.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034210-68634.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034211-62483.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034211-32867.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034211-96368.png)
∴点
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034211-81424.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034212-94325.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034206-78048.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034212-74387.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034212-53651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034212-70386.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034207-71457.png)
核心考点
试题【(本小题13分)已知两定点满足条件的点P的轨迹是曲线E,直线与曲线E交于A、B两点。如果且曲线E上存在点C,使.(Ⅰ)求曲线的方程;(Ⅱ)求AB的直线方程;(Ⅲ】;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/20191024/20191024034155-83003.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034146-44066.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034146-19343.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034146-68810.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034146-57304.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034146-94947.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034147-76238.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034146-94947.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034147-22661.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034147-31065.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034147-10579.png)
(I) 求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034146-94947.png)
(II)求点
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034147-22661.png)
(III) 设
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034147-95671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034147-95671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034147-26870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034147-95671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034147-10757.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034139-13641.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034139-47655.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034139-86019.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034139-92365.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034140-23097.png)
A.
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034140-46306.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034140-26062.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034140-87193.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034141-80131.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034133-90613.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034133-42198.png)
A.![]() | B.![]() | C.![]() ![]() | D.![]() ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034126-29525.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034126-36858.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034126-47452.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034127-67511.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034127-30756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034127-44563.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034127-62830.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024034128-61419.png)
A.2 | B.![]() | C.![]() | D.![]() |
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