Answer
Foci: $( \pm 1,1)$ and vertices : $(\pm\sqrt 2,1)$
Work Step by Step
$2y^{2}-4y=-x^{2}$
$\frac{x^{2}}{2}+\frac{(y-1)^{2}}{1}=1$, which represents an equation of ellipse with $c^{2}=2-1$
or, $c=1$
Hence, Foci: $( \pm 1,1)$ and vertices : $(\pm\sqrt 2,1)$
