conic section

conic section or conic , curve formed by the intersection of a plane and a right circular cone (conical surface). The ordinary conic sections are the circle , the ellipse , the parabola , and the hyperbola . When the plane passes through the vertex of the cone, the result is a point, a straight line, or a pair of intersecting straight lines; these are called degenerate conic sections. There are many examples of the conic sections, both in nature and in technology. The orbits of planets and satellites are elliptical, and parallel reflectors (e.g., in telescopes) are parabolic in shape.

conic section A figure obtained by slicing a cone. There are four different types of conic section. If the cone is cut perpendicular to its axis, the resulting figure is a circle. If the cut is not perpendicular to the axis but still produces a closed curve, the curve is an ellipse. If the cone is cut parallel to one of its sloping sides, the resulting curve is a parabola, which is not closed. If the angle of cut is tilted still further, the open figure obtained is a hyperbola. An ellipse has an eccentricity less than 1; a circle is a special case of an ellipse, where the eccentricity is 0. A parabola has an eccentricity of exactly 1. A hyperbola has an eccentricity greater than 1. The orbits of celestial bodies are conic sections.