TOPICS

# Conic Section

The conic sections are the classes of nondegenerate curves generated by the intersections of a plane with one or two nappes of a cone. A conic section can also be realized as the zero set of a quadratic equation in two variables.

Conic section is a high school-level concept that would be first encountered in a pre-calculus course covering conic sections. It is listed in the California State Standards for Mathematical Analysis.

### Examples

 Circle: A circle is the set of points in a plane that are equidistant from a given center point. Ellipse: A conic section with eccentricity less than one. It resembles a squashed circle. Hyperbola: A hyperbola is a conic section with eccentricity greater than one and consists of two separate branches. Parabola: A parabola is a conic section with eccentricity equal to one. Parabolas appear as the graphs of quadratic equations and the trajectories of projectiles.

### Prerequisites

 Cone: A cone is a pyramid with a circular cross section. Cross Section: The cross section of a solid is a plane figure obtained by the intersection of that solid with a plane. Curve: A curve is a continuous map from a one-dimensional space to an n-dimensional space. Loosely speaking, the word "curve" is often used to mean the function graph of a two- or three-dimensional curve.