Let S1=x2+y2+2gx−4y+4=0 S2=x2+y2+6x+2fy+12=0 and S3=x2+y2+10y+20=0 For radical centre, we have ‌S1=S2=S3 ⇒S1−S2=0 ⇒(2g−6)x−(4+2f)y−8=0 Since, (−1,−1) is the radical centre. ‌∴(2g−6)(−1)−(4+2f)(−1)−8=0 ‌⇒‌‌g−f=1 ‌