2x-5y-1=0
x+4y-7=0
y=1,x=3
A(3,1)
过A直线y-1=k(x-3)
y=-x/k
-x/k-1=k(x-3)
-x-k=k^2(x-3)
(k^2+1)x=3k^2-k
x=(3k^2-k)/(k^2+1)
y=(3k-1)/(k^2+1)
x^2+y^2=2
[(3k^2-k)^2+(3k-1)^2]/(k^2+1)^2=2
(3k-1)^2=2(k^2+1)
9k^2-6k+1=2k^2+2
7k^2-6k-1=0
(7k+1)(k-1)=0
k=1或k=-1/7
y-1=(x-3)或 y-1= -(x-3)/7