(1) There are three non-degenerate conics: the ellipse, the parabola , and the hyperbola.

(2) Menaechmus is famed for his discovery of the conic sections and he was the first to show that ellipses, parabolas , and hyperbolas are obtained by cutting a cone in a plane not parallel to the base.

(3) Long-period comets can have orbits ranging from eccentric ellipses to parabolas to even modest hyperbolas.

(4) The solutions to the equations describing the motions produced by this law are called conic sections - ellipses, hyperbolae and parabolae - which you get by intersecting a plane and a cone.

(5) Newton and Kepler left behind the tools for constructing flight paths from simple conic sections - bits of parabolas , hyperbolas, ellipses, and the ubiquitous circle - and their use is now a highly developed art.