In geometry, a locus (Latin for "place", plural loci) is a collection of points which share a property. For example a circle may be defined as the locus of points in a plane at a fixed distance from a given point.
A locus may alternatively be described as the path through which a point moves to fulfill a given condition or conditions. So, for example, a circle may also be defined as the locus of a point moving so as to remain at a given distance from a fixed point.
The term occurs in complex dynamics as:
In general, a proof that a locus is particular curve has two parts. The first part is to show that every point on the curve satisfies the condition of the locus and second part is to show that every point that satisfies the condition is on the curve. For example, to show that the locus of points equidistant between two given points is their perpendicular bisector, one must show: