If $(0,6)$ and $(0,3)$ are respectively the vertex and focus of a parabola, then its equation is

The vertex and focus of the parabola are $(0,6)$ and $(0,3)$ respectively. Clearly, axis is $Y$-axis. $\therefore$ Latusrectum $=4$ (Distance between vertex and focus) $$ =4 \sqrt{(0-0)^{2}+(6-3)^{2}}=12 $$ Also, the vertex is on the right hand side of the focus, so the parabola opens downward. Hence, equation of the parabola is $$ \begin{aligned} (x-0)^{2} &=-12(y-6) \\ x^{2} &=-12 y+72 \\ \Rightarrow \quad & x^{2}+12 y &=72 \end{aligned} $$