The document discusses how to find the equation of a locus by considering an arbitrary point (x,y) on the curve and relating x and y based on the description of the curve. It provides examples of locus problems, such as finding the equation for all points equidistant from two given points, where the sum of distances to two given points is a constant, where the sum of squared distances to two given points is a constant, all points on a line with a given slope through a given point, and where the difference of distances to two given points is a constant.

1. 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)

2. 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.

3. Examples:
Find an equation for the set of all points (x, y) satisfying the
given conditions
5.It is equidistant from (5, 8) and (-2, 4).
6.The sum of its distances from (0, 4) and (0, -4) is 10.
7.The sum of the squares of its distances from (3, 0 ) and
(-3, 0) is 50.
8.It is on the line having slope of 2 and containing the point
(3, -2).
9.The difference of its distances from (3, 0) and (-3, 0) is 2.