Question

What are the equations for the asymptotes of this hyperbola? =1 64 = 55 O Av=1 V5. --VES 5 ty=-V55 5 x, y= 5 V 73 S O B.V=V73 -- = O c. v=zt, y=- OD 1 = 8, y = - 8 Too colon

Answer 1

The Solution:

Given the equation of the hyperbola below:

$\frac{x^2}{9}-\frac{y^2}{64}=1$

We are required to find the equation for the asymptotes of the above hyperbola.

By formula, the equation for the asymptotes is

$\begin{gathered} y=\pm\frac{b}{a}x \\ \text{Where} \\ a^2=9 \\ a=\pm3 \\ b^2=64 \\ b=\pm8 \end{gathered}$

Substituting these values in the formula above, we get

$\begin{gathered} y=\pm\frac{8}{3}x \\ \text{This becomes} \\ y=+\frac{8}{3}x\text{ or }y=-_{}\frac{8}{3}x \end{gathered}$

Therefore, the correct answer is option D.