## Calculus 8th Edition

$\dfrac{x^{2}}{2}+\dfrac{y^{2}}{4}=1$, which represents an equation of ellipse.
From the given vertices : $(0,\pm2)$ we find that $b=2$ and from foci: $( 0,\pm 2)$ we have $c=\sqrt 2$ and $a=\sqrt 2$ Hence, $\dfrac{x^{2}}{2}+\dfrac{y^{2}}{4}=1$, which represents an equation of ellipse.