(1)根据圆心到直线的距离等于半径建立关于a的方程,求出a值.
(2)根据
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823231506369575.png)
,借助弦长公式可求得圆心到直线的距离,从而利用点到直线的距离公式建立关于a的方程,求出a值.
解:将圆C的方程
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823231506057798.png)
配方得标准方程为
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823231506525711.png)
,则此圆的圆心为(0 , 4),半径为2. ……………………………2分
(1) 若直线
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823231506088280.png)
与圆C相切,则有
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823231506572740.png)
. …………………………4分
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823231506400506.png)
. ……………………6分
(2) 解法一:过圆心C作CD⊥AB, ………7分
则根据题意和圆的性质,得
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232315066031905.png)
…………………10分
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823231506634441.png)
.……………12分
(解法二:联立方程
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232315066501186.png)
并消去
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823231506665309.png)
,得
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232315067281249.png)
.
设此方程的两根分别为
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823231506743299.png)
、
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823231506853334.png)
,则用
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232315068681329.png)
即可求出a.)
∴直线
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823231506088280.png)
的方程是
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823231506447637.png)
和
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823231506463564.png)
.…………………………14分