Answer
Foci :
$(0,-2\sqrt{3})$ and $(0, 2\sqrt{3})$.
Work Step by Step
Write the equation in standard form:
$4x^{2}+16y^{2}=64\qquad/64$
$\displaystyle \frac{4x^{2}}{64}+\frac{16y^{2}}{64}=1$
$\displaystyle \frac{x^{2}}{16}+\frac{y^{2}}{4}=1$
Major axis parallel to the x-axis, horizontal,
$a=4, b=2$
Foci are $c$ units right and $c$ units left of center,
$c^{2}=16-4=12$
$c=\sqrt{12}=2\sqrt{3}$
Foci :
$(0,-2\sqrt{3})$ and $(0, 2\sqrt{3})$.
