Answer
See image:
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Work Step by Step
Divide the equation with $3$
$\displaystyle \frac{y^{2}}{2}-\frac{x^{2}}{8}=1,\ \quad$
We recognize the standard equation of a hyperbola.
Foci on the y-axis: $\quad \displaystyle \frac{y^{2}}{a^{2}}-\frac{x^{2}}{b^{2}}=1\quad \Rightarrow a=\sqrt{2},\ b=2\sqrt{2}$
Center-to-focus distance: $\quad c=\sqrt{a^{2}+b^{2}}=\sqrt{2+8}= \sqrt{10}$
Foci: $\quad (0, \pm c)= \quad (0, \pm\sqrt{10})$
Vertices: $\quad (0, \pm\sqrt{2})$
Asymptotes: $\quad y=\displaystyle \pm\frac{a}{b}x=\pm\frac{\sqrt{2}}{2\sqrt{2}}x=\pm 2x$
$y=\displaystyle \pm\frac{1}{2}x$
