题目内容
已知直线l:x-y+4=0与圆C:(x-1)2+(y-1)2=2,则圆C上各点到l距离的最小值为________,最大值为________.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054120537344.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054120537344.png)
由圆的标准方程得圆的圆心C(1,1),半径长r=
,则圆心C(1,1)到直线l的距离d=
=2
>
=r,所以直线l与圆C相离,
则圆C上各点到l距离的最小值为d-r=2
-
=
,最大值为d+r=2
+
=3
.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054120537344.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054120569549.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054120537344.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054120537344.png)
则圆C上各点到l距离的最小值为d-r=2
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054120537344.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054120537344.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054120537344.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054120537344.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054120537344.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054120537344.png)
![](http://thumb.zyjl.cn/images/loading.gif)
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