Answer
See image:
Work Step by Step
Divide the equation with $8$
$\displaystyle \frac{y^{2}}{8}-\frac{x^{2}}{8}=1,\ \quad$
Here, we recognize the standard equation of a hyperbola.
Foci on the y-axis: $\quad \displaystyle \frac{y^{2}}{a^{2}}-\frac{x^{2}}{b^{2}}=1\quad \Rightarrow a=b=\sqrt{8}=2\sqrt{2}$
Center-to-focus distance: $\quad c=\sqrt{a^{2}+b^{2}}=\sqrt{8+8}=4$
Foci: $\quad (0, \pm c)= \quad (0, \pm 4)$
Vertices: $\quad (0, \pm 2\sqrt{2})$
Asymptotes: $\quad y=\displaystyle \pm\frac{a}{b}x=\pm\frac{2\sqrt{2}}{2\sqrt{2}}x=\pm x$
$y=\pm x$
