Let C1(h,k) be the center of the circle. Circle touches the x-axis then its radius is r1=k Also circle touches the circle with centre C2(0,3) and radius r2=2 ‌∴‌‌|C1C2|=r1+r2 ‌⇒√(h−0)2+(k−3)2=|k+2| ‌⇒‌‌h2−10k+5=0 Change h to x and k to y ⇒‌‌x2−10y+5=0 It is a parabola.