过抛物线y²=4x的焦点且斜率=2的直线K交抛物线A,B两点,求L的方程及线段AB的长

过抛物线y²=4x的焦点且斜率=2的直线K交抛物线A,B两点,求L的方程及线段AB的长

y^2=4x,p=2,F(1,0)
y=2*(x-1)
L:2x-y-2=0
x=(y+2)/2
y^2=4x=4*(y+2)/2
y^2-2y-4=0
yA+yB=2,yA*yB=-4
(yA-yB)^2=(yA+yB)^2-4yA*yB=2^2-4*(-4)=20
(xA-xB)^2=(1/4)*(yA-yB)^2
AB^2=(1+1/4)*(yA-yB)^2=(5/4)*20=25
|AB|=5