By the parent 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 power 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 centre line of the circles. This locus is called the chordal or the radical axis of the circles.