题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232543-65509.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232543-38850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232544-95732.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232544-51236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232544-62499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232544-81680.png)
(Ⅰ)求轨迹W的方程;
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232545-62180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232545-72502.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232545-19914.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232545-51468.png)
求出直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232545-19914.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232546-20252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232546-25637.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232546-95335.png)
解析
试题分析:(Ⅰ)因为A,B两点关于x轴对称,
所以AB边所在直线与y轴平行.
设
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232546-85648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232547-19404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232547-64994.png)
所以点M的轨迹W的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232547-51474.png)
(Ⅱ)假设存在,设
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232547-81544.png)
当直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232548-86145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232548-57382.png)
消去y得
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232548-26176.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232548-80461.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232549-60833.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232549-96874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232546-25637.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232549-85835.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232549-91098.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232550-68353.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232550-33628.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232550-89738.png)
要使
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232551-54268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232551-21316.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232551-55248.png)
所以不存在直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232546-25637.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232551-54268.png)
当直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232551-83118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232552-17048.png)
综上:不存在直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232546-25637.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232551-54268.png)
点评:求动点的轨迹方程时要先设出所求点坐标,找到其满足的关系式,进而整理化简,最后验证是否有不满足的点;直线与圆锥曲线相交时,常联立方程组,利用韦达定理找到方程的根与系数的关系,进而将所求问题转化为用交点坐标表示
核心考点
试题【已知的顶点A在射线上,、两点关于x轴对称,0为坐标原点,且线段AB上有一点M满足当点A在上移动时,记点M的轨迹为W.(Ⅰ)求轨迹W的方程;(Ⅱ)设是否存在过的直】;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/20191025/20191025232538-68022.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232538-23356.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232531-53224.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232525-22740.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232525-19258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232525-75341.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232514-54601.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232514-42480.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232514-42312.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232514-42480.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232514-76863.jpg)
(I)若点C的纵坐标为2,求
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232515-40735.png)
(II)若
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232515-39450.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232457-90378.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232458-86214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232458-54415.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232458-10064.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232458-19046.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232459-78133.jpg)
(Ⅰ) 若
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232459-18183.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232459-66683.png)
(Ⅱ)若点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232459-30505.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232500-49156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232500-64204.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232500-62988.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025232500-89525.png)
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