1. The locus of a point which is equidistant from two fixed points A and B is the perpendicular bisector of the line segment AB.
2. The locus of a point which is at a constant distance from a fixed point is a circle.
3. If the join of two fixed points A, B subtends a right angle at P, then the locus of P is a circle on AB as diameter.
4. Given A and B are two fixed points, the locus of a point P such that the area of Δ PAB is a constant is a pair of lines parallel to AB.
5. If A, B are two fixed points and P is a moving point such that (PA/PB) = k (k ≠ 1), then the locus of the point P is a circle.
6. The locus of the point which moves equidistant from a fixed point and fixed straight line is a parabola.
7. Let A, B be two fixed points and PA + PB = k
(a) If k > AB, then the locus of P is an ellipse
(b) If k = AB, then the locus of P is line segment AB
(c) If k < AB, then the locus of P does not exist
8. Let A, B be two fixed points and |PA – PB| = k
(a) If k > AB, then the locus of P does not exist
(b) If k = AB, then the locus of P is line through A and B except line segment AB
(c) If k < AB, then the locus of P is a hyperbola