Answer:
[tex]y = \frac{3}{4} x \: \: and \: \: y = - \frac{3}{4} x[/tex]
Step-by-step explanation:
The given hyperbola has equation:
[tex] \frac{ {x}^{2} }{16} - \frac{ {y}^{2} }{9} = 1[/tex]
The equations of asymptotes of the hyperbola.
[tex] \frac{ {x}^{2} }{ {a}^{2} } - \frac{ {y}^{2} }{ {b}^{2} } = 1[/tex]
is
[tex]y = \pm \: \frac{b}{a} x[/tex]
Comparing the given equation to the standard equation of the hyperbola we have:
[tex] \frac{ {x}^{2} }{ {4}^{2} } - \frac{ {y}^{2} }{ {3}^{2} } = 1[/tex]
This implies that:
a=4 and b=3
The asymptote equations are:
[tex]y = \pm \frac{3}{4}x [/tex]
Or
[tex]y = \frac{3}{4} x \: \: and \: \: y = - \frac{3}{4} x[/tex]
