Answer
Foci:
$(-\displaystyle \frac{\sqrt{299}}{4},0)$ and $(\displaystyle \frac{\sqrt{299}}{4},0)$.
Work Step by Step
Major axis parallel to the x-axis, horizontal
$a^{2}=\displaystyle \frac{25}{4}$
$a=\displaystyle \frac{9}{2}$
$b^{2}=\displaystyle \frac{25}{16},$
$b=\displaystyle \frac{5}{4}$
Center: (0,0)
Vertices: $(h-a, k),\quad (h+a, k) $
$(-\displaystyle \frac{9}{2}, 0),\quad (\displaystyle \frac{9}{2}, 0) $
Foci are $c$ units right and $c$ units left of center,
where $c^{2}=a^{2}-b^{2}:$
$c^{2}=a^{2}-b^{2}=\displaystyle \frac{324}{16}-\frac{25}{16}=\frac{299}{16}$
$c=\displaystyle \frac{\sqrt{299}}{4}\approx 4.3$
Foci:
$(-\displaystyle \frac{\sqrt{299}}{4},0)$ and $(\displaystyle \frac{\sqrt{299}}{4},0)$.
