conic section or conic (kŏn`ĭk), curve formed by the intersection of a plane and a right circular cone cone or conical surface, in mathematics, surface generated by a moving line (the generator) that passes through a given fixed point (the vertex) and continually intersects a given fixed curve (the directrix).
..... Click the link for more information. (conical surface). The ordinary conic sections are the circle circle, closed plane curve consisting of all points at a given distance from some fixed point, called the center. A circle is a conic section cut by a plane perpendicular to the axis of the cone.
..... Click the link for more information. , the ellipse ellipse, closed plane curve consisting of all points for which the sum of the distances between a point on the curve and two fixed points (foci) is the same. It is the conic section formed by a plane cutting all the elements of the cone in the same nappe.
..... Click the link for more information. , the parabola parabola (pərăb`ələ)
..... Click the link for more information. , and the hyperbola hyperbola (hīpûr`bələ)
..... Click the link for more information. . 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

Any two-dimensional curve traced by the intersection of a right circular cone with a plane. If the plane is perpendicular to the cone's axis, the resulting curve is a circle. Intersections at other angles result in ellipses, parabolas, and hyperbolas. The conic sections are studied in Euclidean geometry to analyze their physical properties and in analytic geometry to derive their equations. In either context, they have useful applications to optics, antenna design, structural engineering, and architecture.