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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, a line is the locus of points equidistant from two fixed points.
The conic sections may be defined in terms of loci:
- A circle is the locus of points from which the distance to the center is a given value, the radius.
- An ellipse is the locus of points, the sum of the distances from which to the foci is a given value.
- A parabola is the locus of points, the distances from which to the focus and to the directrix are equal.
- A hyperbola is the locus of points, the difference of the distances from which to the foci is a given value.
Very complex geometric shapes may described as the locus of zeros of a function or polynomial. Thus, for example, the quadric surfaces are defined as the loci of zeros of the quadratic polynomials. More generally, the locus of zeros of a set of polynomials are called an algebraic variety, the properties of which are studied in the branch of mathematics known as algebraic geometry.
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