Answer
$\displaystyle \frac{x^{2}}{33}+\frac{y^{2}}{49}=1$
Work Step by Step
With the given information,
the foci are $c=4$ units above/below the point (0,0)
the major axis is vertical, $a=7$
so the standard form the equation is
$\displaystyle \frac{(x-h)^{2}}{b^{2}}+ \displaystyle \frac{(y-k)^{2}}{a^{2}}=1$
$(h,k)=(0,0)$
$a=7$
$c=4$
From $b^{2}=a^{2}-c^{2}$
$b^{2}=49-16=33$
so the equation is
$\displaystyle \frac{x^{2}}{33}+\frac{y^{2}}{49}=1$