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

Let C1(x1,y1)  be the locus of centre. r=|y1|  (∵ circle touches x-axis.) And C2(0,3), r2=2 ∴C1C2=r1+r2  (∵ two circles touches)⇒(x1−0)2+(y1−3)2=y1+2 Squaring on both sides⇒x12+y12+9−6y1=y12+4+4y1 ⇒x12=10y1−5 ∴ locus is x2=10y−5 ∴ It represents parabola.