section_path: Circle of Apollonius/Generalised circles
section_name: Generalised circles
paragraph_text: Generalised circles
  
  If C is the midpoint of the segment AB, then the collection of points P satisfying the Apollonius condition | A P | | B P | = | A C | | B C | {\displaystyle {\frac {|AP|}{|BP|}}={\frac {|AC|}{|BC|}}} is not a circle, but rather a line.
  
  Thus, if A, B, and C are given distinct points in the plane, then the locus of points P satisfying the above equation is called a "generalised circle." It may either be a true circle or a line. In this sense a line is a generalised circle of infinite radius.