题目
题型:不详难度:来源:
已知定点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034548-95105.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034548-38515.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034549-11739.gif)
(I)求动点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034548-38515.gif)
(II)过点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034549-57284.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034549-98934.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034549-37257.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034549-69488.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034549-61658.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034549-72889.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034549-46156.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034549-72889.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034548-38515.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034549-43509.gif)
(II)当直线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034549-98934.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034549-26378.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034550-14707.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034550-57976.gif)
故,在x轴上存在定点C(1,0) ,使得
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034549-46156.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034550-25338.gif)
(当动点P与两定点A,B共线时也符合上述结论)
所以动点P的轨迹为以A,B为焦点,实轴长为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034550-31884.gif)
所以,轨迹G的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034549-43509.gif)
(Ⅱ)假设存在定点C(m,0),使
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034549-46156.gif)
①当直线l不与x轴垂直时,设直线l的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034550-73100.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034550-80308.gif)
由题意知,
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034550-59843.gif)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034550-81259.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034550-47618.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034551-97868.gif)
于是
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034551-45023.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034551-95487.gif)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034551-76648.gif)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034551-87807.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034551-35866.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034552-86346.gif)
要是使得
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034549-46156.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034550-14707.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034550-57976.gif)
②当直线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034549-98934.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034549-26378.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034550-14707.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034550-57976.gif)
故,在x轴上存在定点C(1,0) ,使得
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034549-46156.gif)
核心考点
试题【(本小题满分12分)已知定点,动点满足: . (I)求动点的轨迹的方程;(II)过点的直线与轨迹交于两点,试问在轴上是否存在定点,使得 为常数.若存在,求出点的】;主要考察你对曲线与方程的应用等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034539-74697.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034539-97677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034540-12582.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034536-75334.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034536-15745.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034529-76666.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034529-13079.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034530-11826.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034530-95556.gif)
标为( )
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034530-71691.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034530-17939.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034531-98277.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034531-75101.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034531-10798.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034531-68152.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034531-97913.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034532-43966.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034523-63421.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034523-54963.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034523-69340.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034523-68754.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034523-92233.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034523-63421.gif)
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