Equation of parabola whose vertex is (2, 5) and focus (2, 2) is

$\mathrm{V}=\left(2,5\right) \mathrm{S}=\left(2,2\right)$

In vertex and focus x-coordinates are equal eq. of parabola symmetric to Y-axis and $\mathrm{a}=\mathrm{SA}=\sqrt{0+9}=3$

Eq. of parabola

 $$\begin{gathered} {\left(\mathrm{x}-\mathrm{h}\right)}^2=-4\mathrm{a}\left(\mathrm{y}-\mathrm{k}\right) \\ {\left(\mathrm{x}-2\right)}^2=-12\left(\mathrm{y}-5\right) \end{gathered}$$