Locus (mathematics)
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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, the conic sections are 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.
Other geometrical shapes are defined in terms of loci:
- A line is the locus of points equidistant from two fixed pointsTemplate:Geometry-stub