Answer
See image:
Work Step by Step
Divide the equation with $4225$
$\displaystyle \frac{x^{2}}{25}+\frac{y^{2}}{169}=1$
$\displaystyle \frac{x^{2}}{(5)^{2}}+\frac{y^{2}}{(13)^{2}}=1$, which is of the form $\quad \displaystyle \frac{x^{2}}{b^{2}}+\frac{y^{2}}{a^{2}}=1 \quad (a\gt b)$
$\Rightarrow$ the foci are on the y-axis.
Center-to-focus distance: $\quad c=\sqrt{a^{2}-b^{2}}=\sqrt{169-25}=12$
Foci: $\quad(0, \pm c)= \quad(0, \pm 12)$
Vertices: $\quad (0, \pm a)= \quad (0, \pm 13)$
