Locus (mathematics)

In mathematics, a locus (Latin for "place", plural loci) is a collection of points which share a common property. A locus of points usually forms a continuous figure or figures. For example, the conic sections are defined in terms of loci:

  1. A circle is the locus of points from which the distance to the center is a given value, the radius.
  2. An ellipse is the locus of points, the sum of the distances from which to the foci is a given value.
  3. A parabola is the locus of points, the distances from which to the focus and to the directrix are equal.
  4. A hyperbola is the locus of points, the difference of the distances from which to the foci is a given value.

Other geometrical shapes are defined in terms of loci:

  1. A line is the locus of points equidistant from two fixed points
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See also: Locus (mathematics), Circle, Conic sections, Ellipse, Focus (geometry), Geometry, Hyperbola, Latin, Line (mathematics)