## Quick Reference

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.

*Subjects:*
Mathematics.