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

问题描述:

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

设A(x0,y0)、B(x1,y1)的中点是M,将A、B代抛物线再相减,得:y1²-y2²=2p(x1-x2),(y1-y2)/(x1-x2)=2p/(y1+y2)=2p/(2y0)=p/y0,即k=p/(y0).