I wrote a game with a rocket that orbits a planet, and you can change the orbit with thrusters. As part of it I draw the predicted orbit for the rocket. To do this I compute the eccentricity vector, then the eccentricity e, then the major and minor axis of the ellipse or hyperbola as appropriate. With these values computing the equation of the orbit's elliptical or hyperbolic path is straightforward. This all works great in my app. However it's entirely unclear to me how to compute the parabolic path when e=1. I know its the limit of the elliptical orbit as e approaches 1, but I don't know how to compute the parameters when e=1 exactly. Specifically, how do I compute the distance from the focus to the vertex of the parabola?