Given equations of circle are c1:x2+y2+2gx+2fy+c=0 The centre is O(−g,−f),r1=√g2+f2−c c2:x2+y2+2gx+2fy+csin2α+(g2+f2)cos2α=0 Centre O(−g,−f) r2=√g2+f2−csin2α−g2cos2α−f2cos2α =√g2+f2−c×sin‌α since, the two circles are concentric as shown in figure.