Question

Find the equations for the asymptotes of the hyperbola.

Answer 1

Answer:

$y = \frac{3}{4} x \: \: and \: \: y = - \frac{3}{4} x$

Step-by-step explanation:

The given hyperbola has equation:

$\frac{ {x}^{2} }{16} - \frac{ {y}^{2} }{9} = 1$

The equations of asymptotes of the hyperbola.

$\frac{ {x}^{2} }{ {a}^{2} } - \frac{ {y}^{2} }{ {b}^{2} } = 1$

is

$y = \pm \: \frac{b}{a} x$

Comparing the given equation to the standard equation of the hyperbola we have:

$\frac{ {x}^{2} }{ {4}^{2} } - \frac{ {y}^{2} }{ {3}^{2} } = 1$

This implies that:

a=4 and b=3

The asymptote equations are:

$y = \pm \frac{3}{4}x$

Or

$y = \frac{3}{4} x \: \: and \: \: y = - \frac{3}{4} x$