TOPICS

# Locus

A locus is the set of all points (usually forming a curve or surface) satisfying some condition. For example, the locus of points in a plane that are equidistant from a given point is a circle.

Locus 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

 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. Surface: A surface is a two-dimensional piece of three-dimensional space.