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