Browse Questions

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

$\begin{array}{1 1}(A)\;a\; hyperbola \\(B)\;a\; parabola \\(C)\;an\; ellipse \\(D)\;a \;circle \end{array}$

Let centre $=(h,k)$
Since $c_1c_2=r_1 \pm r_2$
$\therefore \sqrt {(h-0)^2+(k-3)^2}= |k \pm 2|$
=> $h^2=5(2k-5)$
$\therefore$ Locus is $x^2=5(2y-1)$
Which is a parabola.
Hence b is the correct answer.