Q.If A(2, 0) and B(0, 3) are two points, find the equation of the locus of point P such that AP = 2BP.

A locus is the set of every point in a plane that satisfies one fixed geometric condition — for example, all points equidistant from two fixed points, or all points a fixed distance from a fixed point. Familiar figures are secretly loci: a perpendicular bisector is the locus of points equidistant from a segment's endpoints, an angle bisector is the locus of points equidistant from the angle's arms, and a circle is the locus of points a fixed distance from its centre. An equation in x and y is called the equation of a locus when the set of points whose coordinates satisfy it is exactly the locus itself — no more points and no fewer. To find it, you take a general point P(x,y), translate the defining geometric condition (usually an equality of distances) into an algebraic equation using the distance formula, and simplify. This turns a geometric description into an algebraic one that can be manipulated, graphed, and classified — recognising, for instance, that a particular locus turns out to be a circle or a straight line.