NIMCET 2015 Question Paper with solutions

Let the centre of circle is (b, and radius of circle is k Center of another circle (0, 3) and radius is 2
Both circles touch each other
$\therefore \sqrt{{\left(\mathit{h}-0\right)}^2+{\left(\mathit{k}-3\right)}^2}=\mathit{k}+2$
$\Rightarrow \sqrt{{\mathit{h}}^2+{\mathit{k}}^2-6\mathit{k}+9}=\mathit{k}+2$
$\Rightarrow {\mathit{h}}^2+{\mathit{k}}^2-6\mathit{k}+9={\mathit{k}}^2+4\mathit{k}+4$
$\Rightarrow {\mathit{h}}^2=10\mathit{k}-5$
$\Rightarrow \mathit{x}=10\mathit{y}-5$ which represent equation of parabola
∴ Locus of centre of circle is parabola.