AN EQUATION OF A LOCUS

Prepared by:Prof. Teresita P. Liwanag – Zapanta

B.S.C.E., M.S.C.M., M.Ed. (Math-units), PhD-TM (on-going)

FINDING AN EQUATION OF A LOCUS

Since an equation of a curve is a relationship satisfied by the x and y coordinates of each point on the curve (but by no other point), we need merely consider an arbitrary point (x,y) on the curve and give the description of the curve in terms of x and y.

Examples:

Find an equation for the set of all points (x, y) satisfying the given conditions

1.It is equidistant from (5, 8) and (-2, 4).2.The sum of its distances from (0, 4) and (0, -4) is 10.3.The sum of the squares of its distances from (3, 0 ) and (-3, 0) is 50.4.It is on the line having slope of 2 and containing the point (3, -2).5.The difference of its distances from (3, 0) and (-3, 0) is 2.