In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions. The concept of locus is crucial in geometry. Suppose X and Y are two fixed points in two-dimensional coordinate planes. If a point M moves on this plane in such a manner that its distance from the points X and Y are always equal, then the point M will trace out a definite path on the plane. Thus, a moving point M traces out a definite path on the given plane if it satisfies some specified geometrical conditions. Such a path traced out by a moving point M on a plane is called its locus. Locus is the path traced by a moving point satisfying certain conditions.
The locus of an equation is a curve containing those points, and only those points, whose coordinates satisfy the equation. Sometimes the curve may be defined by a set of conditions rather than by an equation, though an equation may be derived from the given conditions. A locus is a set of points that contains all the points, and only the points, that satisfy the condition, or conditions, required to describe a geometric figure. The word locus is Latin for place or location. All the shapes such as circle, ellipse, parabola, hyperbola, etc. are defined by the locus as a set of points.
In real-life you must have heard about the word ‘location’. The word location is derived from the word locus itself. Locus defines the position of something. When an object is situated somewhere, or something happened at a place, is described by locus. For example, the area has become a locus of opposition to the government.
Locus of Points
The locus of points defines a shape in geometry. Suppose, a circle is the locus of all the points which are equidistant from the centre. Similarly, the other shapes such as an ellipse, parabola, hyperbola, etc. are defined by the locus of the points.The locus is defined only for curved shapes. These shapes can be regular or irregular. Locus is not described for the shapes having vertex or angles inside them.