令k=1/a
x-y/a-3=0
y=-ax+3a
代入
(a^2+1)x^2-(2+6a^2)+(9a^2-8)=0
x1+x2=(2+6a^2)/(a^2+1)
y1+y2=-a(x1+x2)+6a=4a/(a^2+1)
中点D[(1+3a^2)/(a^2+1),2a/(a^2+1)]
OD^2=(9a^4+10a^2+1)/(a^2+1)^2
x1x2=(9a^2-8)/(a^2+1)
(x1-x2)^2=(x1+x2)^2-4x1x2=(28a^2+33)/(a^2+1)^2
(y1-y2)^2=[(-ax1+3a)-(-ax2+3a)]^2=a^2(x1-x2)^2
所以AB^2=(a^2+1)(x1-x2)^2=(28a^2+33)/(a^2+1)
AB^2=4OD^2
(28a^2+33)/(a^2+1)=4(9a^4+10a^2+1)/(a^2+1)^2
a^2=29/8
k^2=8/29
x-√(8/29)y-3=0
x+√(8/29)y-3=0