Question

Find the equations for the asymptotes of the hyperbola.

Answer 1

`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`