Answer
$$ {y^{2}}-\dfrac {x^{2}}{3}=1$$
Work Step by Step
Equation of hyperbola with a format of
$$\dfrac {y^{2}}{a^{2}}-\dfrac {x^{2}}{b^{2}}=1\left( a > 0,b > 0\right) $$
Foci are $\left( 0,\pm c\right) ;c^{2}=a^{2}+b^{2}$
Vertices are $\left( 0,\pm a\right) $
Given vertices $(0,\pm1)$ we find $a=1$ and given foci $(0,\pm2)$ we find $c=2$
$\Rightarrow c^{2}=a^{2}+b^{2}\Rightarrow 2^{2}=1^{2}+b^{2}\Rightarrow b^2=3$
Then the equation will be
$$\Rightarrow {y^{2}}-\dfrac {x^{2}}{3}=1$$
