抛物线大题,已知抛物线C：y^2=2px(p＞0),O为原点,C上有不同于O的两个点A、B,k(OA)、k(OB)分别表

y^2=2px
Ay^2=2pAx Ay/Ax=2p/Ay
By^2=2pBx By/Bx=2p/By
Ay^2-By^2=2p(Ax-Bx)
AB斜率k=(Ay-By)/(Ax-Bx)=2p/(Ay+By)
k(OA)+k(OB)=λ
Ay/Ax+By/Bx=λ
k(OA)*k(OB)=-λ
(Ay/Ax)(By/Bx)=-λ
(Ay/Ax)^2-λ(Ay/Ax)-λ=0
Ay/Ax=λ/2+λ√5/2 By/Bx=λ/2-λ√5/2 或 Ay/Ax=λ/2-λ√5/2 By/Bx=λ/2+λ√5/2
2p/Ay=λ/2+λ√5/2 2p/By=λ/2-λ√5/2 2p/Ay=λ/2-λ√5/2 2p/By=λ/2+λ√5/2
Ay=4p/(1+√5) By=4p/(1-√5) Ay=4p/(1-√5) By=4p/(1+√5)
k=2p/[4p*(1/(1+√5)+1/(1-√5))]
=1/[2*(1/2)]=1

设A为(yA^2/(2p),yA)，B为(yB^2/(2p),yB)。
有，k(OA)=(yA-0)/[yA^2/(2p)-0]=2p/yA, k(OB)=2p/yB,
当yA^2/(2p)不=yB^2/(2p)时，直线AB的斜率k(AB)=(yA-yB) / [yA^2/(2p)-yB^2/(2p)]=2p/(yA+yB)
又，k(OA)+k(OB)=2p(1/yA+1...