题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023453-18996.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023453-41395.gif)
(1) 求动点 M的轨迹 C的方程;
(2)已知直线
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023453-81345.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023453-68551.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023454-22738.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023454-11856.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023454-71215.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023453-68551.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023453-81345.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023453-68551.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023454-67249.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023455-23150.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023455-98360.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023455-92310.gif)
∴点 M的轨迹C是以
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023455-71123.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023456-40378.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023456-37018.gif)
∴ 动点M的轨迹 C的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023456-23133.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023456-90347.gif)
(2)由(1)知,轨迹C是椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023456-23133.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023457-13433.gif)
设满足条件的直线
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023457-75286.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023457-96740.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023457-75286.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023457-54892.gif)
则直线
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023457-96740.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023458-55326.gif)
将①代入椭圆方程并整理得:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023458-23912.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023458-39565.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023458-76487.gif)
将②代入椭圆方程并整理得:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023459-81283.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023459-19196.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023459-99586.gif)
由△BDE是等腰直角三角形得
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023459-38005.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023500-56647.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023500-74233.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023500-87026.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023500-65643.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023501-15629.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023501-68371.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023501-34194.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023501-28367.gif)
∵方程④
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023502-70228.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023502-95410.gif)
∴即满足条件的直线
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023457-75286.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023457-96740.gif)
解析
核心考点
试题【已知:向量,O为坐标原点,动点M满足:.(1) 求动点 M的轨迹 C的方程;(2)已知直线、都过点,且,、与轨迹C分别交于点D、E.是否存在这样的直线、,使得△】;主要考察你对平面向量应用举例等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023448-55813.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023448-55813.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023448-79371.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023448-74029.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023449-82934.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023448-74029.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023449-72467.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023449-83387.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023442-67370.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023442-79631.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023443-33099.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023442-79631.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023443-56721.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023432-48976.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023432-48976.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023432-48976.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023432-27290.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023432-65038.png)
A.
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023432-14782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023433-49279.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023433-14617.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023433-60727.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023423-20333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023423-79416.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023424-49777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023424-10146.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023424-99998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023424-24409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023424-99998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023424-20240.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023412-30914.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023412-82803.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023412-95128.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105023412-49700.png)
A.1 | B.2 | C.-1 | D.-2 |
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