Answer
$\displaystyle \frac{x^{2}}{7}+\frac{y^{2}}{16}=1$
Work Step by Step
With the given information,
the foci are $c=3$ units above/below the point (0,0)
the major axis is vertical, $a=4$
so the standard form the equation is
$\displaystyle \frac{(x-h)^{2}}{b^{2}}+ \displaystyle \frac{(y-k)^{2}}{a^{2}}=1$
$(h,k)=(0,0)$
$a=4$
$c=3$
From $b^{2}=a^{2}-c^{2}$
$b^{2}=16-9=7$
so the equation is
$\displaystyle \frac{x^{2}}{7}+\frac{y^{2}}{16}=1$