Find the equation of the locus of the center of the circle which touches the X axis, and also touches the Circle with Center(0,3) and Radius 2 units. Also prove that this locus is a Parabola.

Please help on how to start the problem.

My approach was finding 2 points which are definitily present on the locus (by rough plot) and then proving y^2 is proportional to x, but I guess that won't work.