A circle touches the x-axis and also touches the circle with centre (0, 3) and radius 2. The locus of the centre of the circle is

Let C1(h, k) be the center of the circleThe circle touches the x-axis.' Then its radius is r1=kAlso, the circle touches the circle with center C2(O,3) and radius r2: 2. Therefore,C1C2=r1+r2or (h−0)2+(k−3)2=|k+2|Squaring, we geth2−10k+5=0Therefore, the locus isx2−10y+5=0 which is a parabola