求过直线x+y+4=o与圆x2+y2+4X-2y-4=o的交点,且与直线y=x相切的圆的方程.

Answer 1

M:x^2+y^2+4x-2y-=0......(1)
M(-2,1),r=3
x+y+4=0,k=-1
CM:y=x+3
C(a,a+3)
y=x
x-y=0
R^2=d^2=|a-a-3|^2/2=4.5
C:(x-a)^2+(y-a-3)^2=4.5......(2)
(1)-(2):
2(2+a)x+2(2+a)y-2a^2-6a-8.5=0
(-2a^2-6a-8.5)/[2(2+a)]=4
a=-3.5
C(-3.5,-0.5)
(x+3.5)^2+(y+0.5)^2=4.5