Answer
Foci:$\quad(0,\pm\sqrt{2})$
Eccentricity$:\qquad e =\displaystyle \frac{\sqrt{2}}{2}$
Directrices$:\quad y=\pm 2\sqrt{2}$
Graph:
Work Step by Step
$2x^{2}+y^{2}=4\qquad/\div 4$
$\displaystyle \frac{x^{2}}{2}+\frac{y^{2}}{4}=1,\qquad$
We have a vertical major axis.
$ a=2,b=\sqrt{2}$,
Foci:$\quad(0,\pm c)$
$c=\sqrt{a^{2}-b^{2}}=\sqrt{4-2}=\sqrt{2}$
Eccentricity$:\qquad e=\displaystyle \frac{c}{a}=\frac{\sqrt{2}}{2}$
Directrices$:\quad y=0\displaystyle \pm\frac{a}{e}$
$y=\displaystyle \pm\frac{2}{(\frac{\sqrt{2}}{2})}$
$y=\pm 2\sqrt{2}$
