(1)设动点的坐标为P(x,y),则
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122523305244.gif)
=(x,y-1),
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122523414247.gif)
=(x,y+1),
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122523492243.gif)
=(1-x,-y)
∵
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122523305244.gif)
·
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122523414247.gif)
=k|
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122523492243.gif)
|
2,∴x
2+y
2-1=k[(x-1)
2+y
2] 即(1-k)x
2+(1-k)y
2+2kx-k-1=0.
若k=1,则方程为x=1,表示过点(1,0)是平行于y轴的直线.
若k≠1,则方程化为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122523585758.gif)
,表示以(-
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122523617289.gif)
,0)为圆心,以
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122523632310.gif)
为半径的圆.
(2)当k=2时,方程化为(x-2)
2+y
2=1.∵2
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122523305244.gif)
+
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122523414247.gif)
=2(x,y-1)+(x,y+1)=(3x,3y-1),
∴|2
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122523305244.gif)
+
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122523414247.gif)
|=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122523726622.gif)
.又x
2+y
2=4x-3,∴|2
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122523305244.gif)
+
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122523414247.gif)
|=
∵(x-2)
2+y
2=1,∴令x=2+cosθ,y=sinθ,
则36x-6y-26=36cosθ-6sinθ+46=6
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122523788251.gif)
cos(θ+φ)+46∈[46-6
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122523788251.gif)
,46+6
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122523788251.gif)
],
∴|2
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122523305244.gif)
+
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122523414247.gif)
|
max=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122523882534.gif)
=3+
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122523788251.gif)
,|2
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122523305244.gif)
+
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122523414247.gif)
|
min=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122523944522.gif)
=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122523788251.gif)
-3.