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