A variable circle passes through the fixed point (2,0) and touches the y-axis . Then the locus of its centre is
A circle
An Ellipse
Now (h−2)2+k2=h2⇒h2+4−4h+k2=h2 ⇒ k2 = 4 h - 4. Hence the locus of centre is y2= 4x - 4, which is a parabola.