Everyone knows by now that a conic section is the figure formed when a plane intersects a right circular cone. Most everyone also knows that there are many different ways to describe a conic, geometrically and algebraically. What one seldom sees is the derivation of those descriptions from the fundamental definition. Using Dandelin Spheres it is easy to accomplish this for an ellipse. What I have never seen is a proof, based on the fundamental definition, of the equivalence of the ratio of the distances of a point on the conic to the focus and to the directrix, or even a definition of the directrix itself. Can anyone supply or direct me to such information? Thanks.