Answer
$\displaystyle \frac{y^{2}}{4}-\frac{x^{2}}{1}=1,\quad$(hyperbola)
Foci: $\quad (0, \pm\sqrt{5})$
Vertices: $\quad (0, \pm 2)$
Asymptotes: $\quad y=\pm 2x$
Work Step by Step
Hyperbola, vertical axis.
Foci on the y-axis: $\quad \displaystyle \frac{y^{2}}{a^{2}}-\frac{x^{2}}{b^{2}}=1$
Center-to-focus distance: $\quad c=\sqrt{a^{2}+b^{2}}$
Foci: $\quad (0, \pm c)$
Vertices: $\quad (0, \pm a)$
Asymptotes: $\quad y=\displaystyle \pm\frac{a}{b}x$
Of the offered equations,
$\displaystyle \frac{y^{2}}{4}-\frac{x^{2}}{1}=1\quad$ has this form. $a=2,\ b=1$
Center-to-focus distance: $\quad c=\sqrt{4+1}=\sqrt{5}$
Foci: $\quad (0, \pm\sqrt{5})$
Vertices: $\quad (0, \pm 2)$
Asymptotes: $\quad y=\displaystyle \pm\frac{2}{1}x=\pm 2x$
