已知抛物线Y^2=2px,p(x0,y0)直线L过P点与抛物线交于A,B两点。若弦AB恰被P点平分,求证直线l的斜率为 p/y0

A(X1,Y1) B(X2,Y2)
所以X1+X2=2X0
Y1+Y2=2Y0
设直线斜率K
Y-Y0=K(X-XO)
A，B两点在直线上
Y1-Y0=K(X1-X0)
Y2-Y0=K(X2-X0)
想减得Y1-Y2=K（X1-X2）
Y1^2=2PX1
Y2^2=2PX2
相减得(Y1-Y2)(Y1+Y2)=2P(X1-X2)
(Y1-Y2)/(X1-X2) * 2YO=2P
K* 2YO=2P

K=P/Y0

A(X1,Y1) B(X2,Y2)
X1+X2=2X0
Y1+Y2=2Y0
直线斜率K
Y-Y0=K(X-XO)
A，B两点在直线上
Y1-Y0=K(X1-X0)
Y2-Y0=K(X2-X0)
想减得Y1-Y2=K（X1-X2）
Y1^2=2PX1
Y2^2=2PX2
相减得(Y1-Y2)(Y1+Y2)=2P(X1-X2)
(Y1-Y2)/(X1-X2) * 2YO=2P
K* 2YO=2P