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