Editing Locus (mathematics) (section)

==Examples in plane geometry==
Examples from plane geometry include:
* The set of points equidistant from two points is a [[perpendicular bisector]] to the [[line segment]] connecting the two points.<ref>George E. Martin, ''The Foundations of Geometry and the Non-Euclidean Plane'', Springer-Verlag, 1975.</ref>
* The set of points equidistant from two intersecting lines is the [[union (set theory)|union]] of their two [[angle bisector]]s.
* All [[conic section]]s are loci:<ref>{{citation |first1=Henry Parr |last1=Hamilton |title=An Analytical System of Conic Sections: Designed for the Use of Students |publisher=Springer |year=1834}}.</ref>
** [[Circle]]: the set of points at constant distance (the [[radius]]) from a fixed point (the [[center (geometry)|center]]).
** [[Parabola]]: the set of points equidistant from a fixed point (the [[focus (geometry)|focus]]) and a line (the [[directrix (conic section)|directrix]]).
** [[Hyperbola]]: the set of points for each of which the absolute value of the difference between the distances to two given foci is a constant.
** [[Ellipse]]: the set of points for each of which the sum of the distances to two given foci is a constant

Other examples of loci appear in various areas of mathematics. For example, in [[complex dynamics]], the [[Mandelbrot set#Formal definition|Mandelbrot set]] is a subset of the [[complex plane]] that may be characterized as the [[connectedness locus]] of a family of polynomial maps.