Form 3 Mathematics Bab 8: Loci in Two Dimensions
A locus (plural: loci) is a set of points whose locations satisfy one or more specific conditions in two-dimensional space.
The locus of a point moving at a fixed distance $r$ from a fixed point $A$ is a circle with centre $A$ and radius $r$.
The locus of a point moving at an equal distance from two fixed points $A$ and $B$ is the perpendicular bisector of the line segment $AB$.
The locus of a point moving at a fixed distance $d$ from a straight line $AB$ consists of a pair of parallel lines located distance $d$ on either side of $AB$.
The locus of a point moving at an equal distance from two parallel lines $AB$ and $CD$ is a single parallel line passing midway between $AB$ and $CD$.
The locus of a point moving at an equal distance from two intersecting lines $AB$ and $AC$ is the angle bisector of the angle formed by those lines ($\angle BAC$).
The intersection of two loci is the point or set of points that simultaneously satisfies the conditions of both loci.