A Collection of Loci Using Two Fixed Points

Abstract

The use of dynamic geometry software in constructing loci with various conditions placed on the distances from two fixed points is described, where either (1) the sum of the squares, (2) the difference of the squares, (3) the ratio, or (4) the product of the two distances is constant. The equation of each locus analytically is also derived. In the first three cases, the loci are circles or lines. In the fourth case, the locus is a spiric section described by a quartic equation.