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