Obtain the parametric equations of the circle ${\mathrm{x}}^2+{\mathrm{y}}^2-6\mathrm{x}+4\mathrm{y}-12=0$.

$\text{ circle is }{\mathrm{x}}^2+{\mathrm{y}}^2-6\mathrm{x}+4\mathrm{y}-12=0$
$\text{ Centre }\mathrm{C}=(-\mathrm{g},-\mathrm{f})=(3,-2)$
$\text{ Radius }\mathrm{r}=\sqrt{{\mathrm{g}}^2+{\mathrm{f}}^2-\mathrm{c}}=\sqrt{9+4+12}=5$
Parametric equations of the circle are
$\mathrm{x}={\mathrm{x}}_1+\mathrm{rcos}\mathrm{\theta },\mathrm{y}={\mathrm{y}}_1+\mathrm{rsin}\mathrm{\theta }$
$\text{ Where }\left({\mathrm{x}}_1,{\mathrm{y}}_1\right)\text{ is centre, }\mathrm{r}\text{ is the radius of the circle ' }\mathrm{\theta }\text{ ' is parameter }$
$\begin{array}{l}\therefore \mathrm{x}=3+5\cos \mathrm{\theta }\\ \mathrm{y}=-2+5\sin \mathrm{\theta }\end{array}$