Circle(s) touching x-axis at a distance 3 from the origin and having an intercept of length 27 on y-axis, is (are)

Let the equation of the circle be x2+y2+2gx+2fy+c=0. It touches x-axis at a distance 3 from the origin. Therefore, c=g2 and the circle passes through (±3, 0).∴    9±6g+c=0⇒    9±6g+g2=0⇒(g±3)2=0⇒g=−3∴    c=g2⇒c=9The circle cuts an intercept of length 27 on y-axis.∴ 2f2−c=27⇒f2−9=7⇒f=±4Hence, the equations of the circles are   x2+y2−6x±8y+9=0