CONIC SECTION

also called Conic, in geometry, any curve produced by the intersection of a plane and a right circular cone. Depending on the angle of the plane relative to the cone, the intersection is a circle, an ellipse, a hyperbola, or a parabola. Special (degenerate) cases of intersection are that of the plane passing through the apex and no other part of the cone, in which a single point is produced, and that of the plane passing through the apex intersecting the cone elsewhere, in which one or two intersecting lines are produced. Sections of other surfaces may also be conicse.g., those formed by planes passing through elliptical cones and parabolic cylinders. Conics may be described as plane curves that are the paths (loci) of a point moving so that the ratio of its distance from a fixed point (the focus) to the distance from a fixed line (the directrix) is a constant, called the eccentricity of the curve. If the eccentricity is zero, the curve is a circle; if equal to one, a parabola; if less than one, an ellipse; and if greater than one, a hyperbola.