Determine the constraint that must be followed. For example, a student may be asked to find "the locus of points that represents the circle." In this case, the underlying constraint would be that all points follow the formula for a circle.
Graph a smooth curve that encompasses all the points set forth by the constraint. From the example above, you would draw a circle.
Ensure that all points possible are shown in the representation of the constraint. In the case of a circle, a line drawn with equal radius around the center point encompasses all possible points and therefore fulfills the requirement that all possible points be represented.
Prove that every point falls within the constraint set forth previously. It is simple, when examining a circle, to state that the formula of the circle was used to generate the graph and therefore the locus of points presented represents a line that follows the constraint.