The point P(x, y) is a general point on the Cartesian plane. The x and y are denote the abscissa and ordinate of a point respectively. The co-ordinates of the general point P, both x and y are variables therefore the point P is also called a variable point. When a point P moves under certain conditions then the path traced out by the point P is called the locus of the point. The locus of a variable point P (x, y) is called a curve. In coordinate geometry, we deal with two types of fundamental problems.
1. Given locus of a variable point (geometrical condition), to find the corresponding equation (algebraic relation)
2. Given an equation, to find the corresponding curve.
Definition of locus: A locus is the set of points (and only those points) that satisfy the given consistent geometric condition(s).
      From the above definition, it follows that:
(i) Every point satisfying the given conditions is a point on the locus.
(ii) Every point on the locus satisfies the given conditions.
Note: Locus is a Latin word which means 'location' or 'place'.The plural of locus is loci. A set of geometric conditions is said to be 'consistent', if there is atleast one point satisfying the set of conditions.
      For example, when A = (2, 0) and B = (5, 0), the condition 'the sum of the distances of a point from A and B is equal to 3' is consistent. Whereas the condition 'the sum of distances of a point Q from A and B is equal to 2' is not consistent. The locus of the point equidistant from three non collinear points. The locus consists of only one point. Which is the circumcentre of the triangle formed the three non-collinear points.
Equation of Locus: The equation of a locus we mean an algebraic description of the locus. It is obtained by translating the geometric conditions satisfied by the points on the locus, into equivalent algebraic conditions.
Procedure for find locus

      An equation of a locus is an algebraic description of the locus. This can be obtained in the following way.
 I) P(x, y) or P(h, k) or P(x1, y1) or P(α, β) be a point on the locus. Select point P suitable to geometric condition(s).
 II) Write the geometric condition(s) to be satisfied by P in terms of an equation or inequation in symbols.
 III) Apply the proper formula of co-ordinate geometry and translate the geometric conditio (s) into an algebraic equation.
 IV) Simplify the equation so that it is free from radicals.