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