Given Ends of Major axis $\;(\pm3,0)$, Ends of Minor Axis $\;(0, \pm 2)$, $a=4$ and $c = 3$
$c^2 = a^2 - b^2 \rightarrow 9 = 16 - b^2 \rightarrow b = \sqrt{7}$
We therefore can write the equation of the ellipse as $\;\large\frac{x^2}{4^2}$$+\large\frac{y^2}{\sqrt 7 ^2}$$=1$
$\Rightarrow$ The equation of the ellipse is $\large\frac{x^2}{16}$$+\large\frac{y^2}{7}$$=1$