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. Show Classification of conic sectionsAll conic sections fall into the following categories: Nondegenerate conic sections
Degenerate conic sectionsIf the cutting plane passes through the vertex of the cone, the result is a degenerate conic section. Degenerate conics fall into three categories:
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Definitions of conic sections in terms of foci and directrices
Definitions of conic sections in terms of Cartesian coordinates
See Also
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