Let centre of circle be C(−g,−f), then equation of circle passing through origin be x2+y2+2gx+2fy=0
∴ Distance, d=|−g−3|=g+3 In △ABC,‌‌(BC)2=AC2+BA2 ⇒‌‌g2+f2=(g+3)2+22 ⇒‌‌g2+f2=g2+6g+9+4 ⇒‌‌f2=6g+13 Hence, required locus is y2+6x=13