The Greeks discovered
the properties that define conics in terms of points and lines. These properties
are important tool for current day problems with the behaviors of atoms, molecules
and outer space. Particles
that move under the influence of an inverse square force field has a path that
is described by conic sections.
An Introduction to Conic Sections - Analytic Geometry
Each of the geometric figures are obtained by intersecting a double-napped right circular cone with a plane. Thus, the figures are called conic sections or conics. If the plane cuts completely across one nappe of the cone and is perpendicular to the axis of the cone, the curve of the section is called a circle.
An ellipse is the set of all points in a plane, the sum of the distances from two fixed points in the plane is constant.
Many comets have elliptical orbits.
A parabola is the set of all points in a plane equidistant from a fixed point and a fixed line in the plane.
The hyperbola is the set of all points in a plane. The difference of whose distance from two fixed points in the plane is the positive constant.