题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042820-20905.gif)
A,B恒有
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042820-39882.gif)
(1)求弦AB中点M的轨迹方程
(2)以AP和PB为邻边作矩形AQBP,求点Q轨迹方程
(3)若x,y满足Q点轨迹方程,求
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042820-29749.gif)
答案
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042820-33181.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042821-15463.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042821-80774.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042821-46654.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042821-94254.gif)
C(0,0)则
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042822-40836.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042822-37302.gif)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042822-73086.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042822-69968.gif)
化简得
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042822-89057.gif)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042820-33181.gif)
(2)以AP,PB相邻边作矩形AQBP,设Q(x,y)则AB,PQ互相平分于M点,
则
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042823-50596.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042823-83791.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042823-86526.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042823-22713.gif)
(3)设:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042823-52653.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042824-42592.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042824-50258.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042824-53476.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042824-34842.gif)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042812-58095.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042812-47751.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042813-35220.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042804-92669.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042805-20852.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042805-86416.gif)
(Ⅰ)求椭圆C1的方程及双曲线C2的离心率;
(Ⅱ)在第一象限内取双曲线C2上一点P,连结AP交椭圆C1于点M,连结PB并延长交椭圆C1于点N,若
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042805-98970.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042805-48699.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042805-64295.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042749-56763.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042750-68538.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042750-36588.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042750-85807.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042750-62384.gif)
①
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042750-75690.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042751-76093.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042751-22650.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042751-61466.gif)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042749-56763.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042751-28836.gif)
(2)过点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042752-51041.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042752-10765.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042752-18092.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042752-47729.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042744-53131.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042744-24154.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042744-93771.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042744-19135.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042730-64725.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042730-48274.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042730-74894.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042731-26576.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042731-74705.gif)
(1) 设点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042731-74705.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042731-97983.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042731-49343.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042731-52070.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042732-92769.gif)
(2) 设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042732-54077.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042732-93741.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042730-74894.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042732-43212.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042732-41651.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042732-43212.gif)
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