A variable circle passes through the fixed point (2, 0) and touches the y-axis. Then, the locus of its centre, is

Let the variable circle bex2+y2+2gx+2fy+c=0                         ... (i)It passes through (2, 0) and touches y-axis.∴ 4+4g+c=0     and c=f2⇒ 4+4y+f2=0Hence, the locus of the centre  (- g, - f) of circle (i) is4−4x+y2=0⇒ y2=4(x−1), which is a parabola.