The family of circles through the intersection of S1=0 and S2=0 is S1+lambdaS2=0. If L=0 is a line and S=0 is a circle, then S+lambdaL=0 gives the family of circles through the intersection of the line and circle. Coaxial circles share the same radical axis. Their centres are collinear, and every pair in the system has the same radical axis.