x^2+y^2-4x+2y=0 (1)
x^2+y^2-2x-4=0 (2)
(2)-(1)
2x-2y-4=0
x-y-2=0
y=x-2,代入(2)
x^2-2x+(x-2)^2-4=0
x(x-3)=0
x=0 y=-2
x=3 y=1
2x+4y=1
x=(1-4y)/2
设圆心坐标((1-4y)/2,y)
[(1-4y)/2-0]^2+(y+1)^2=[(1-4y)/2-3]^2+(y-1)^2
整理,得
32y=-24
y=-3/4
x=[1-4(-3/4)]/2=2
半径^2=(2-0)^2+(-3/4+1)^2=65/16
所求圆方程为(x-2)^2+(y+3/4)^2=65/16