a^2+b^2+4a-8b+20=0
(a^2+4a+4)+(b^2-8b+16)=0
即(a+2)^2+(b-4)^2=0
可得a=-2,b=4
代回为x^2+y^2-4-2axy=(x-y)^2-4=(x-y-2)(x-y+2)