Answer
Ellipse
Foci: $( \pm 1,1)$
Vertices : $(\pm\sqrt 2,1)$
Work Step by Step
$2y^{2}-4y=-x^{2}$
$\frac{x^{2}}{2}+\frac{(y-1)^{2}}{1}=1$, equation of ellipse
$c^{2}=2-1$
$c=1$
Foci: $( \pm 1,1)$
Vertices : $(\pm\sqrt 2,1)$