Given two points A and B in the plane and a constant k, the locus of all points P such that AP/PB=k is a circle. A circle obtained like this is an Apollonius' circle. Taking k=1 gives a straight line, so either this value must be excluded or, in this context, a straight line must be considered to be a special case of a circle. In the figure, k=2.
http://www.jimloy.com/cindy/apoll.htm An interactive webpage where you can alter the ratio to see how the circle changes.