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