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.