If a circle of radius 2 touches X-axis at (1,0)  then its centre may be

Let x2+y2+2gx+2fy+c=0  be the circle Since the circle touches x-axis at (1,0)  theng2=c  and r=|f| .2=|f| ⇒f=±2 Since circle passes through (1,0)  then⇒1+2g+c=0 ⇒1+2g+g2=0  (∵c=g2) ⇒(g+1)2=0 ⇒g=−1 ∴ centre=(−g,−f)=(1,±2) ∴ centre is (1,2)  or (1,−2)