Question

求两圆x^2+y^2-2x-6y+9=0与x^2+y^2-2mx-2(m-1)y+2m^2-2m=0的圆心距的最小值,并

Answer 1

x^2+y^2-2x-6y+9=0

(x-1)^2+(y-3)^2=1

圆心(1,3)

x^2+y^2-2mx-2(m-1)y+2m^2-2m=0

(x-m)^2+(y-m+1)^2=1

圆心(m ,m- 1)

圆心距^2

=(m-1)^2+(m-1-3)^2

=2m^2-10m +17

=2(m-2.5)^2+4.5

m=2.5,最小值3√2 /2

3√2 /2>1+1

两圆的位置关系：外离