chordal

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

K_{1}(x,\,y):=(x-x_{1})^{2}+(y-y_{1})^{2}-r_{1}^{2}=0

is equal to $K_{1}(a,\,b)$ and with respect to the circle

K_{2}(x,\,y):=(x-x_{2})^{2}+(y-y_{2})^{2}-r_{2}^{2}=0

equal to $K_{2}(a,\,b)$ . Thus the locus of all points $(x,\,y)$ having the same with respect to both circles is characterized by the equation

K_{1}(x,\,y)=K_{2}(x,\,y).

This reduces to the form

2(x_{2}-x_{2})x+2(y_{2}-y_{1})y+k=0,

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