Conic section

Revision as of 10:48, 27 May 2008 by JBL (talk | contribs) (someone please quickly classify degenerate conics)

A conic section is any of the geometric figures that can arise when a plane intersects a cone. (In fact, one usually considers a "two-ended cone," that is, two congruent right circular cones placed tip to tip so that their axes align.) As is clear from their definition, the conic sections are all plane curves, and every conic section can be described in Cartesian coordinates by a polynomial equation of degree two or less.

Classification of conic sections

All conic sections fall into the following categories:

Nondegenerate conic sections

  • A parabola is formed when the cutting plane makes an angle with the axis that is equal to the angle between the element of the cone and the axis.
  • An hyperbola is formed when the cutting plane makes an angle with the axis that is smaller than the angle between the element of the cone and the axis.

Degenerate conic sections

If the cutting plane passes through the vertex of the cone, the result is a degenerate conic section.

See Also