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.