Conic Sections

Conic Sections, in geometry, two-dimensional curves produced by slicing a plane through a three-dimensional right circular conical surface. This surface is similar to two hollow cones held tip to tip. If the plane cuts the surface at right angles to the surface’s axis (a line passing through the exact center of the cones), a circle is produced. A slice parallel to a surface of the cones produces a parabola. Any cut between these two types of slices results in an ellipse. More vertical cuts that intersect both cones produce hyperbola. For detailed information on each type of conic section, see Circle, Parabola, Ellipse, and Hyperbola.

Passing the plane through the conical surface in certain specific ways produces degenerate conics, which include a point, a line, a pair of parallel lines, and a pair of intersecting lines. If the surface is cut at the point where the two cones meet by a plane perpendicular to the axis, for example, a point is produced.

The Greek mathematician Apollonius of Perga, who lived from the early 300s to the late 200s bc, wrote eight books with the title Conic Sections. These books superseded previous work on the subject by Aristarchus of Sámos and Euclid.