题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115248-77060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115249-37751.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115249-23926.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115249-37751.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115249-51796.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115249-23926.png)
A.![]() | B.![]() | C.![]() | D.![]() |
答案
解析
分析:根据抛物线的方程求得焦点坐标和准线的方程,设出所求圆的圆心,表示出半径,则圆的方程可得,把M,F点的坐标代入整理求得h,和g,则圆的方程可得.
解:抛物线y2=4x的焦参数p=2,所以F(1,0),直线l:x=-1,即x+1=0,
设经过点M(4,4)、F(1,0),且与直线l相切的圆的圆心为Q(g,h),
则半径为Q到,l的距离,即1+g,所以圆的方程为(x-g)2+(y-h)2=(1+g)2,
将M、F的坐标代入,得(4-g)2+(4-h)2=(1+g)2,(1-g)2+(0-h)2=(1+g)2,
即h2-8h+1=10g①,
h2=4g②,②代入①,
得3h2+16h-2=0,
解得h1=
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115250-92850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115251-22505.png)
代入②得g1=
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115251-43876.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115251-68561.png)
所以满足条件的圆有两个:
(x-
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115251-43876.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115250-92850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115251-74878.png)
(x-
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115251-68561.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115251-22505.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115252-80414.png)
故选C
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115232-60198.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115232-12955.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115232-92376.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115232-16660.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115232-49622.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115233-78199.jpg)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115233-35609.png)
(2)记直线MN的斜率为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115233-82912.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115233-56699.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115234-95774.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115226-80323.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115226-30276.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115227-27860.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115227-42078.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115227-83900.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115227-14877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115228-77950.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115228-38161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115228-51630.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115211-97756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115211-79393.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115211-27625.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115211-44626.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115211-44626.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115212-66974.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115212-26701.png)
(1)若直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115212-66974.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115212-25400.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115212-69701.png)
(2)设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115212-90509.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115212-13177.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115213-93728.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115200-42325.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115200-46301.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115201-70687.png)
A 4 B 2 C –4 D –2
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115129-89063.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115129-66077.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115129-96730.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115129-47917.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115130-79986.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115130-30798.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115130-85084.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115130-29606.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025115130-78934.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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