Answer
Foci:
$(0, -\sqrt{21})$ and $(0, \sqrt{21})$.
Work Step by Step
Write the equation in standard form:
$25x^{2}+4y^{2}=100\qquad/100$
$\displaystyle \frac{25x^{2}}{100}+\frac{4y^{2}}{100}=1$
$\displaystyle \frac{x^{2}}{4}+\frac{y^{2}}{25}=1$
Major axis parallel to the $y$-axis, vertical.
$a=5$
$b=2$
Foci are $c$ units above and $c$ units below the center,
$c^{2}=a^{2}=b^{2}=25-4=21$
$c=\sqrt{21}$
Foci:
$(0, -\sqrt{21})$ and $(0, \sqrt{21})$.
