若抛物线y方=2PX(P>0)的弦PQ中点为(X0,Y0),(Y0≠0),则弦PQ的斜率为
问题描述:
若抛物线y方=2PX(P>0)的弦PQ中点为(X0,Y0),(Y0≠0),则弦PQ的斜率为
答
设P坐标是(X1,Y1),Q坐标是(X1,Y2),则2yo=y1+y2.
Y1^2=2px1
y2^2=2px2
二式相减得:
(y1+y2)(y1-y2)=2p(x1-x2)
即PQ斜率k=(y1-y2)/(x1-x2)=2p/(y1+y2)=2p/2yo=p/yo