The curve described by a point which moves under given condition or conditions is called its locus.

For example, suppose `C` is a point in the plane of the paper and `P` is a variable point in the plane of the paper such that its distance from `C` is always equal to a (say). It is clear that all the positions of the moving point `P` lie on the circumference of a circle whose centre is `C` and whose radius is `a`. The circumference of this circle is, therefore, the "Locus" of point `P` when it moves under the condition that its distance from the point `C` is always equal to constant `a`.

`quad ` Let `A` and `B` be two fixed points in the plane of the paper, and `P` be a variable point in the plane of the paper which moves in such a way that its distance from `A` and `B` is always same. Thus, the "locus" of `P` is the perpendicular bisector of `AB` when it moves under the condition that its distance from `A` and `B` is always equal.

`text(Equation to Locus of a Point :)`

The equation to the locus of a point is the relation which is satisfied by the coordinates of every point on the locus of the point.

`text(Note : Steps to find locus of a point.)`

`text(Step I :)` Assume the coordinates of the point say `(h, k)` whose locus is to be determined.

`text(Step II :)` Write the given condition in mathematical form involving `h, k`.

`text(Step III :)` Eliminate the variable `(s)`, if any.

`text(Step IV : )` Replace `h` by `x` and `k` by `y` in the result obtained in step `III.`

The equation so obtained is the locus of the point which moves under some condition `(s)`.