过原点的直线与圆x平方 y平方-6x 5=0相交于A,B两点,求弦AB的中点M的轨迹方程

x^2 + y^2 - 6x + 5 = 0
y = kx
(1+k)x^2 - 6x + 5 = 0
两根之和x1+x2 = 6/(k+1)
所以A,B中点横坐标 = (x1+x2)/2 = 3/(k+1)
Mx =3/(k+1),My =3k/(k+1)
x+y = 3
x - y = 3
为所求