若圆(x-a))^2+(y-b))^2=b)^2+1平分圆(x+1))^2+(y+1))^2=4的圆周,则a.b应满足什么?

Question

若圆(x-a))^2+(y-b))^2=b)^2+1平分圆(x+1))^2+(y+1))^2=4的圆周,则a.b应满足什么?

Answer 1

(x+1))^2+(y+1))^2=4直径D=4
且为圆(x-a))^2+(y-b))^2=b)^2+1的弦,（-1,-1）为弦中点,（a,b)到弦距离为圆心距
有b^2+1=（D/2）^2+（a+1)^2+(b+1)^2
化简：
满足(a+1)^2+2b+3=0