The Cartesian equation of a locus is a direct relation between x and y.
The parameter 't' is eliminated from the two relations to obtain a functional relation between x and y.
Some times the locus of a point P, according to a given geometrical condition, could give a region.
Example: Locus of a point P(x, y) such that | x | < 1, | y | < 2 constitutes a region inside rectangle.
| x | < 1 ⇒ – 1 < x < 1;
| y | < 2 ⇒ – 2 < y < 2
In order to find the region of | x | < 1 and | y | < 2, first we will draw the lines of x = – 1, x = 1 and y = – 2, y = 2 in the Cartesian plane.
Refer adjacent figure.