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(D) Let the centre of the circle be $(h, k)$.Since the circle touches the $y$-axis,the radius of the circle is equal to the absolute value of the $x$-

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$A$ parabola

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(D) Let the centre of the circle be $(h, k)$.Since the circle touches the $y$-axis,the radius of the circle is equal to the absolute value of the $x$-coordinate of the centre,i.e.,$r = |h|$.Since the circle passes through the point $(2, 0)$,the distance from the centre $(h, k)$ to $(2, 0)$ must equal the radius $r$.Thus,$(h - 2)^2 + (k - 0)^2 = h^2$.Expanding this,we get $h^2 - 4h + 4 + k^2 = h^2$.Simplifying,we get $k^2 = 4h - 4$.Replacing $(h, k)$ with $(x, y)$,the locus of the centre is $y^2 = 4x - 4$,which represents a parabola.

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

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