设B坐标是(yo^2/2p,yo),F坐标是(p/2,0),Q(-p/2,0)
向量BQ=(-p/2-yo^2/2p,-yo),BF=(p/2-yo^2/2p,-yo)
向量BQ*BF=0
即有:(yo^2/2p)^2-p^2/4+yo^2=0
yo^4/4p^2-p^2/4+yo^2=0
yo^4+4p^2yo^2-p^4=0
(yo^2+2p^2)^2=5p^4
yo^2+2p^2=根号5p^2
yo^2=(根号5-2)p^2
所以,B的横坐标是x1=yo^2/(2p)=(根号5-2)p/2
K(BF)=(0-yo)/(p/2-x1)=-yo/[p/2(1-根号5+2)]=-yo/[p/2(3-根号5)]
故AB的方程是:y-0=-yo/[p/2(3-根号5)]*(x-p/2)
代入到y^2=2px中得到A的横坐标X2,
然后有:|AF|-|BF|=(x2+p/2)-(x1+p/2)=x2-x1.
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