Question

已知圆M：x+y-2mx-2ny+m-1=0与圆N：x+y+2x+2y-2=0交与AB两点,且这两点平分圆N,求圆M的半

Answer 1

AB两点两点平分圆N圆

AB为N圆直径

圆M；

(x-m)^2+(y-n)^2=1+n^2,圆心M(m,n)

圆N：

(x+1)^2+(y+1)^2=4,圆心N（-1,-1）

AB=2R=4

R^2+MN^2=AM^2

4+(m+1)^2+(n+1)^2=n^2+1

M圆心轨迹：

x^2+2x+2y+5=0

2)

x^2+2x+2y+5=0

(x+1)^2+2y+4=0

2y+4