F(1,0)
过点F的直线L,交抛物线C:y^=4x于A,B
L:y=k(x-1)
x=(y+k)/k,xA-xB=(yA-yB)/k
y^2=4x=4*(y+k)/k
ky^2-4y-4k=0
yA+yB=4/k,yA*yB=-4
(yA-yB)^2=(yA+yB)^2-4yA*yB=16(1+k^2)/k^2
(xA-xB)^2=(yA-yB)^2/k^2
AB^2=(xA-xB)^2+(yA-yB)^2
(16/3)^2=(1+1/k^2)*16(1+k^2)/k^2
(k^2-3)*(7k^2+3)=0
k=±√3
直线L的方程:y=±√3(x-1)