The equation ax2+2hxy+by2+2gx+2fy+c=0 represents a circle, the condition will be
a=b and c=0
f=g and h=0
a=b and h=0
f=gand c=0
Comparing ax2+2hxy+by2+2gx+2fy+c=0 with x2+y2+2gx+2fy+c=0 we find that the given equation will represent a circle if a=b and h=0