My problem is this:
"Suppose a plane intersects a right-circular cone in a parabola
with vertex V. Suppose that a sphere is inscribed between the
cone and the plane and is tangent to the plane of the parabola at
point F. Show that the chord to the parabola through F which is perpendicular
to FV has length equal to that of the latus rectum of the parabola. Therefore, F is the focus of the parabola."
I have a very hard time trying to see what conditions the sphere puts on the point F.