已知直线y=(x-2)与抛物线y2=8x相交于两A,B点,F为抛物线的焦点,若/FA/=2/FB/,则k的值为多少?

y^2=8x p/2=2 F(2,0)y=k(x-2)过FFA=2FB Ay=-2By Ay^2=4By^2 Ax=4BxAx+p/2=2(Bx+p/2)Ax=2Bx+24Bx=2Bx+2Bx=1,By=-2√2 Ay=4√2或 By=2√2,Ay=4√2Ax=4,k=(Ay-By)/(Ax-Bx)=2√2 或k=-2√2