Find the equations for the asymptotes of the hyperbola.

Question

asked Apr 1, 2020 5.0k views

1 Answer

Venko · Answer 1 · 2020-04-07T17:48:01+0000

Answer:

$y = (3)/(4) x \: \: and \: \: y = - (3)/(4) x$

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

$y = \pm \: (b)/(a) x$

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:

$y = \pm (3)/(4)x$

Or

$y = (3)/(4) x \: \: and \: \: y = - (3)/(4) x$