Circle of Apollonius

The Circle of Apollonius is a special circle associated with two fixed points, called foci. It consists of all points in the plane where the ratio of distances to these two foci remains constant. For example, if the ratio is 2:1, then every point on this circle is twice as close to one focus as to the other. This concept generalizes the idea of an ellipse and helps in understanding geometric relationships involving distances. The circle reveals how positions relate proportionally, serving as a bridge between distance ratios and geometric loci.