Answer:
[tex]\frac{x^{2}}{4} - y^{2} = 1[/tex] (Option B)
Step-by-step explanation:
The hyperbola has the following vertices: [tex](2,0)[/tex] and [tex](-2,0)[/tex]. The first constant of the hyperbola is:
[tex]2\cdot a = 4[/tex]
[tex]a = 2[/tex]
The other constant is determined by using the standard equation of the hyperbola and replacing all known variables:
[tex]\frac{4^{2}}{4} - \frac{3}{b^{2}} = 1[/tex]
[tex]4 - \frac{3}{b^{2}} = 1[/tex]
[tex]\frac{3}{b^{2}} = 3[/tex]
[tex]b^{2} = 1[/tex]
[tex]b = 1[/tex]
The equation of the hyperbola in standard form is:
[tex]\frac{x^{2}}{4} - y^{2} = 1[/tex] (Option B)
