M:(x-m)^2+(y+n)^2=n^2+1
N:(x+1)^2+(y+1)^2=4
x^2+ y^2-2mx+2ny+m^2-1=0 (1)
x^2+y^2+2x+2y-2=0 (2)
(2)-(1)得,(2m+2)x+(2-2n)y=m^2+1
此直线过N的圆心(-1,-1)
所以
2n-2-2m-2=m^2+1
2n=m^2+2m+5=(m+1)^2+4>=4
n>=2
n^2+1>=5
r最小值为sqrt(n^2+1)=sqrt(5)
M:(x-m)^2+(y+n)^2=n^2+1
N:(x+1)^2+(y+1)^2=4
x^2+ y^2-2mx+2ny+m^2-1=0 (1)
x^2+y^2+2x+2y-2=0 (2)
(2)-(1)得,(2m+2)x+(2-2n)y=m^2+1
此直线过N的圆心(-1,-1)
所以
2n-2-2m-2=m^2+1
2n=m^2+2m+5=(m+1)^2+4>=4
n>=2
n^2+1>=5
r最小值为sqrt(n^2+1)=sqrt(5)