Answer:
Option C. [tex]b=4[/tex]
Step-by-step explanation:
we know that
The equation of a hyperbola with a horizontal transverse axis is
[tex]\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1[/tex]
In this problem we have
[tex]{4x^{2}}-{y^{2}}=16[/tex]
Divide by 16 both sides
[tex]\frac{4x^{2}}{16}-\frac{y^{2}}{16}=1[/tex]
[tex]\frac{x^{2}}{4}-\frac{y^{2}}{16}=1[/tex]
so
[tex]b^{2}=16[/tex]
[tex]b=4[/tex]
