Make a parabola with the origin as the vertex and opening to the right, the focal point f (p/2,0), and the equation of the directrix: x=-p/2. The directrix intersects the X axis at G. If the straight line intersects the parabola at A and B, let FA=m and FB = N. If A intersects AC perpendicular to the directrix at C, B intersects BD perpendicular to the directrix at D.

Extend the extension line where DF intersects with CA to E, the triangle AEF is similar to BDF (AC is parallel to BD), AF=m, BD=n, AE=m, so CE=2m.

In triangle DCE, by using the proportion theorem of parallel lines, there are: GF/CE=BF/BE, from the parabolic property GF=p, so p/(2m)=n/(m+n). By sorting out the scores, we can get1/m+1/n = 2/p.