圆C:x^2+y^2+10x+10y=0
(x+5)^2+(y+5)^2=50
C(-5,-5),r=5√2
设所求圆L的方程为:
(x-a)^2+(y-b)^2=R^2
圆L过点A(0,6):
a^2+(6-b)^2=R^2.(1)
圆L与圆C:x^2+y^2+10x+10y=0切于原点
a^2+b^2=R^2.(2)
LC=R+r=R+5√2
(a+5)^2+(b+5)^2=LC^2=(R+5√2)^2.(3)
解方程组(1)、(2)、(3),得
a=3,b=3,R=3√2
所求圆L的方程为:(x-3)^2+(y-3)^2=18