= Geometric locus
A <geometric locus> is the <set> of points satisfying a specified geometric or algebraic condition in an ambient space. For example, points at a fixed positive distance $r$ from $p$ form a <circle> in the plane and a <sphere> in three dimensions. In the <complex plane>, $|z-z_0|=r$ has Cartesian equation $(x-\operatorname{Re}z_0)^2+(y-\operatorname{Im}z_0)^2=r^2$, proving the <circle> description. A locus can also be a union, such as $x(y-1)=0$, which consists of two lines; domain restrictions in the original equation must be retained when simplifying it.
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