Answer
Foci:
$(0, -\sqrt{5})$ and $(0, \sqrt{5})$.
Work Step by Step
Write the equation in standard form:
$9x^{2}+4y^{2}=36\qquad/36$
$\displaystyle \frac{9x^{2}}{36}+\frac{4y^{2}}{36}=1$
$\displaystyle \frac{x^{2}}{4}+\frac{y^{2}}{9}=1$
Major axis parallel to the $y$-axis, vertical.
$a=3$
$b=2$
Foci are $c$ units above and $c$ units below the center,
$c^{2}=a^{2}-b^{2}=9-4=5$
$c=\sqrt{5}$
Foci:
$(0, -\sqrt{5})$ and $(0, \sqrt{5})$.
