Question

question 9 of 10
what are the equations for the asymptotes of this hyperbola?
$\frac{x^{2}}{9}-\frac{y^{2}}{64}=1$
a. $y = \frac{sqrt{55}}{5}x,y=-\frac{sqrt{55}}{5}x$
b. $y=\frac{8}{3}x,y = -\frac{8}{3}x$
c. $y=\frac{sqrt{73}}{5}x,y=-\frac{sqrt{73}}{5}x$
d. $y=\frac{3}{8}x,y=-\frac{3}{8}x$

Explanation:

Step1: Recall hyperbola asymptote formula

For a hyperbola of the form $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}} = 1$, the equations of the asymptotes are $y=\pm\frac{b}{a}x$.

Step2: Identify values of a and b

In the given hyperbola $\frac{x^{2}}{9}-\frac{y^{2}}{64}=1$, we have $a^{2}=9$ (so $a = 3$) and $b^{2}=64$ (so $b = 8$).

Step3: Find the equations of the asymptotes

Substitute $a = 3$ and $b = 8$ into the asymptote formula $y=\pm\frac{b}{a}x$. We get $y=\frac{8}{3}x$ and $y=-\frac{8}{3}x$.

Answer:

B. $y=\frac{8}{3}x,y =-\frac{8}{3}x$