Explore Locus on MathWorld

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.


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.


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.

Classroom Articles on Conic Sections

  • Conic Section

  • Classroom Articles on Pre-Calculus (Up to High School Level)

  • Asymptote
  • Normal Vector
  • Complex Conjugate
  • Parametric Equations
  • Complex Number
  • Plane
  • Complex Plane
  • Plane Curve
  • Cross Product
  • Polar Coordinates
  • Determinant
  • Range
  • Domain
  • Rational Function
  • Dot Product
  • Reflection
  • e
  • Rotation
  • Exponential Function
  • Rotation Matrix
  • Function
  • Scalar
  • i
  • Spherical Coordinates
  • Imaginary Number
  • Tangent Line
  • Inverse Function
  • Translation
  • Logarithm
  • Vector
  • Natural Logarithm