- There are three non-degenerate conics: the ellipse, the parabola, and the hyperbola.
- 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.
- 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.
- Long-period comets can have orbits ranging from eccentric ellipses to parabolas to even modest hyperbolas.
- 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.