How to Find the Locus of Points

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    • 1). 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.

    • 2). Graph a smooth curve that encompasses all the points set forth by the constraint. From the example above, you would draw a circle.

    • 3). 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.

    • 4). 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.

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