Geometric loci

A geometric locus is the set of all points in a plane (or space) that satisfy a given geometric condition. For example, the locus of points at a fixed distance $r$ from a point $O$ is a circle of radius $r$ centered at $O$.

Important properties

• A locus is usually described by a condition involving distances, angles, or other geometric relationships.

• The locus can be a line, circle, segment, or more complex curve, depending on the condition.

• To find a locus, translate the condition into an equation or geometric construction.