抛物线y^2=2px(p>0)的弦PQ的中点为M(x0,y0)(y0≠0)求直线PQ的斜率

题目

抛物线y^2=2px(p>0)的弦PQ的中点为M(x0,y0)(y0≠0)求直线PQ的斜率

答案

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