Conics arise frequently in phyical simulations, such as plotting the path of a projectiles under the influence of gravity (a parabola), or the near collisions of like-charged particles (hyperbolas).

Conics, like circles posses symmetry, but not nearly to the same extent. A circle is a very special case of conic, it is so special that it is often considered non-generic. Typically a conic will have only one (parabola) or two (ellipse or hyperbola) symmetric axes. As a result, we won't be able to use the same tricks to avoid slope calculations at each point, that we used when drawing circles.

In order to compute the slope at each point we'll need to find derivatives of the disccriminating equation: