By the entry, the power of the point (a,b) with respect to the circle


is equal to  K1(a,b)  and with respect to the circle


equal to  K2(a,b).  Thus the locus of all points (x,y) having the same with respect to both circles is characterized by the equation


This reduces to the form


and hence the locus is a straight line perpendicularMathworldPlanetmathPlanetmathPlanetmath to the of the circles.  This locus is called the chordal or the radical axis of the circles.

Title chordal
Canonical name Chordal
Date of creation 2013-03-22 15:07:50
Last modified on 2013-03-22 15:07:50
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 9
Author PrimeFan (13766)
Entry type Result
Classification msc 51M99
Classification msc 51N20
Synonym radical axis