题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034913-90724.gif)
(1)求点M的轨迹C的方程;
(2)若直线l与曲线C交于A、B两点,且
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034913-64264.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034913-14453.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034913-90724.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034913-90724.gif)
∴ 点M的轨迹方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034913-14453.gif)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034914-79515.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034913-64264.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034914-47426.gif)
∵ A、B均在抛物线上,
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034914-52225.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034914-75828.gif)
由①②可得:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034914-62889.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034915-46847.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034915-52826.gif)
再由
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034914-52225.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034915-13185.gif)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034915-57655.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034916-70989.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034916-23463.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034916-76928.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034916-33576.gif)
∴ 此时AB的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034917-29708.gif)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034917-58836.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034917-84815.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034917-34324.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034918-87471.gif)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034918-94949.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034918-67540.gif)
综上得,直线AB过定点 (5, 0). ...............14分
核心考点
试题【(本小题满分14分)已知动圆与直线相切,且过定点F(1, 0),动圆圆心为M.(1)求点M的轨迹C的方程;(2)若直线l与曲线C交于A、B两点,且(O为坐标原点】;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/20191026/20191026034910-60282.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034910-96167.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034910-82328.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034911-74337.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034911-16702.gif)
A.①③ | B.①② | C.①②④ | D.②④ |
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034855-60594.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034856-27868.gif)
⑴求圆C及椭圆C1的方程;
⑵设圆
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034856-94666.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034856-44968.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034856-20997.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034857-77460.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034857-96986.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034857-61065.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034857-98284.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034858-36589.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034858-86693.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034857-61065.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034858-98492.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034858-27549.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034851-74778.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034851-31968.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034851-60169.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034848-86039.gif)
A.![]() | B.![]() | C.![]() | D.![]() |
已知两定点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034839-55520.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034839-14857.gif)
(1)求点P的轨迹及其方程。
(2)直线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034839-71359.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034840-72201.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034840-25610.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034840-28250.gif)
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