Answer
Foci:
$(0,-2)$ and $(0, 2)$.
Work Step by Step
Major axis parallel to the $y$-axis, vertical.
$a^{2}=\displaystyle \frac{25}{4},$
$a=\displaystyle \frac{5}{2}$
$b^{2}=\displaystyle \frac{9}{4},$
$b=\displaystyle \frac{3}{2}$
Vertices: $(h, k-a),\quad (h, k+a) $
$(0, -\displaystyle \frac{5}{2}),\quad (0, \displaystyle \frac{5}{2}) $
Foci are $c$ units above and $c$ units below the center,
$c^{2}=a^{2}-b^{2}=\displaystyle \frac{25}{4}-\frac{9}{4}=\frac{16}{4}=4$
$c=2$
Foci:
$(0,-2)$ and $(0, 2)$.
