Answer
$${\text{Graph}}\left( {\text{d}} \right)$$
Work Step by Step
$$\eqalign{
& {y^2} - 4{x^2} = 4 \cr
& {\text{Divide both sides by 4}} \cr
& \frac{{{y^2}}}{4} - \frac{{4{x^2}}}{4} = \frac{4}{4} \cr
& \frac{{{y^2}}}{4} - {x^2} = 1 \cr
& {\text{This equation is in standard form}} \cr
& \frac{{{y^2}}}{{{a^2}}} - \frac{{{x^2}}}{{{b^2}}} = 1 \cr
& {\text{Therefore,}} \cr
& \underbrace {\frac{{{y^2}}}{4} - {x^2} = 1 \Rightarrow \frac{{{y^2}}}{{{2^2}}} - {x^2} = 1}_ \Downarrow \cr
& \boxed{a = 2},\boxed{b = 1} \cr
& {\text{Characteristics of the hyperbola }} \cr
& {\text{Orientation}}:{\text{ Vertical transverse axis}} \cr
& {\text{Center}}\left( {0,0} \right) \cr
& \underbrace {{\text{Vertices}}\left( {0, - 2} \right){\text{ and }}\left( {0,2} \right)}_ \Downarrow \cr
& {\text{Vertices}}\left( {0, - 2} \right){\text{ and }}\left( {0,2} \right),{\text{ so}} \cr
& {\text{Graph}}\left( {\text{d}} \right) \cr} $$
