The MathResource
conic section
or conic, n. one of a group of curves formed by the intersection of a plane and a right circular cone, as shown below. This curve is either a circle, if the plane is parallel to the base of the cone; an ellipse, if it is at any other angle at which the intersection is a closed curve; a parabola, if it is parallel to any line joining the vertex of the cone to a point on its base; or a hyperbola, if it is at any other angle. Lines and points are degenerate conics obtained when the intersecting plane includes the vertex of the cone. Conic sections can be conceived geometrically as the loci of points satisfying certain distance relations from a given point, the focus, and a given line, the directrix; the eccentricity is then defined as the ratio of these distances, which is constant for a particular family of similar curves; these properties are described algebraicallly by the conic equations.

Conic sections.