chordal


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

K1(x,y):=(x-x1)2+(y-y1)2-r12=0

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

K2(x,y):=(x-x2)2+(y-y2)2-r22=0

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

K1(x,y)=K2(x,y).

This reduces to the form

2(x2-x2)x+2(y2-y1)y+k=0,

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