Question

AB为抛物线y=2px（p>0）的焦点弦,A（x1,y1）B（x2,y2）,求证x1x2=p/4

Answer 1

思路：y1y2/x1x2=4P^2/y1y2,设焦点弦AB为y=k(x-p/2)代入y^2=2px,得ky^2-2py-kp^2=0,y1y2=-p^2,所以y1y2/x1x2=4P^2/y1y2=4p^2/(-p^2)=-4,

当焦点弦AB与x轴垂直时,此时x1=x2=p/2,y1=p,y2=-p,y1y2/x1x2=-4,综上：y1y2/x1x2的值一定等于-4