已知抛物线 y^2=2px(p>0)过定点M(p,0)作一弦PQ,则1/[MP]^2+1/[MQ]^2线段mp的平方的倒数
问题描述：
已知抛物线 y^2=2px(p>0)过定点M(p,0)作一弦PQ,则1/[MP]^2+1/[MQ]^2
线段mp的平方的倒数
答
设P(2pmm.2pm)Q(2pnn,2pn)PQ:(m+n)y - x -2pmn=0过M(p,0),代入得mn = -1/2MP*MP = (1+(m+n)^2)*(2pm)^2MQ*MQ = (1+(m+n)^2)*(2pn)^21+(m+n)^2 = 1+mm+nn+2mn=mm+nn=>1/[MP]^2+1/[MQ]^2 = (mm+nn)/((mm+nn)*4ppmmnn)=...