过抛物线y^2=4x的焦点F作弦AB,若AF=2BF,则弦AB所在的直线方程

y^2=4x2p=4,p/2=1A(x1,y1),B(x2,y2) AF=2BF y1=-2y2AF=x1+1bf=x2+1x1+1=2(x2+1)x1=2x2+1y1^2=4x1=8x2+4y2^2=4x2y1^2=4y2^28x2+4=16x28x2=4x2=1/2,y2=-√2/2 ,x1=2,y1=√2 k=(y1-y2)/(x1-x2)=(3√2/2)/(3/2)=√2或 x2...过程很正确 但结果是不是有点问题我按照你的过程算出的结果如下：x2=1/2,y2=-√2 ,x1=2,y1=2√2 k=(y1-y2)/(x1-x2)=(3√2)/(3/2)=2√2或x2=1/2,y2=√2, x1=2,y1=-2√2 k=(y1-y2)/(x1-x2)=-2√2AB直线：y=2√2(x-1) 或y=-2√2(x-1)谢谢提醒，你的结果是对的：x2=1/2,y2=-√2 ,x1=2,y1=2√2 k=(y1-y2)/(x1-x2)=(3√2)/(3/2)=2√2或x2=1/2,y2=√2, x1=2,y1=-2√2 k=(y1-y2)/(x1-x2)=-2√2AB直线：y=2√2(x-1) 或y=-2√2(x-1)