If a point moves according to some fixed rule, its co-ordinates will always satisfy some algebraic relation corresponding to the fixed rule. The resulting path (a curve) of the moving point is called the locus of the point. The locus i.e. the curve now contains all the points satisfying the specified condition and no point outside the curve satisfies the condition.

When a point moves in a plane under certain geometrical conditions, the point traces out a path. This path of the moving point is called its locus.

Equation of Locus

The equation to the locus is the relation which exists between the coordinates of all the point on the path, and which holds for no other points except those lying on the path.

Procedure for finding the equation of the locus of a point

(i) If we are finding the equation of the locus of a point P, assign coordinates (h, k) to P.

(ii) Express the given conditions as equations in terms of the known quantities and unknown parameters.

(iii) Eliminate the parameters, so that the eliminant contains only h, k and known quantities.

(iv) Replace h by x, and k by y, in the eliminant. The resulting equation is the equation of the locus of p.

The problem of determining the equation of locus of points every pair of which has constant slope. (see figure given below)

Slope is the tangent (i.e. tan q) of the angle made by a line with the positive x-axis (remember positive) taken in anticlockwise direction from x-axis to the line. For any two points P(x_{1}, y_{1}) and Q(x_{2}, y_{2}).