题目
题型:四川省高考真题难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010226-68426.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010226-65393.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010226-33264.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010226-74090.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010227-55222.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010227-94058.gif)
且
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010227-62151.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010227-68556.gif)
故曲线的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010228-43043.gif)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010228-34408.gif)
由题意建立方程组
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010228-38636.gif)
消去y,得
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010229-79369.gif)
又已知直线与双曲线左支交于
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010229-67996.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010229-43038.gif)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010229-96518.gif)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010230-72844.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010230-73057.gif)
依题意得
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010230-76306.gif)
整理后得
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010230-55424.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010231-27669.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010231-68463.gif)
但
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010231-25495.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010232-24430.gif)
故直线AB的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010232-63763.gif)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010232-82306.gif)
由已知
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010232-16345.gif)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010233-18520.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010233-97597.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010233-14115.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010234-75711.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010234-18836.gif)
∴点
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010234-72542.gif)
将点C的坐标代入曲线E的方程,得
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010234-41104.gif)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010235-42101.gif)
但当
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010235-46632.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010235-86327.gif)
C点的坐标为
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010235-36159.gif)
C到AB的距离为
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010236-98784.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010236-54883.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010236-69203.gif)
核心考点
试题【已知两定点F1(-,0),F2(,0),满足条件的点P的轨迹是曲线E,直线y=kx-1与曲线E交于A、B两点。如果且曲线E上存在点C,使,求m的值和△ABC的面】;主要考察你对平面向量共线条件等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010217-30475.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010217-68380.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010218-45262.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010218-32400.gif)
(2)求动点M的轨迹方程。
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010201-92831.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010201-42200.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010201-46218.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010202-62190.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010202-23510.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104010202-11867.gif)
B.[4,8]
C.(-∞,1]
D.[-1,6]
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