Question

question 15 · 1 point
find the asymptotes of the hyperbola below.
\\(\frac{x^{2}}{9}-\frac{y^{2}}{36}=1\\)
use \\(y = \pm\frac{a}{b}x\\) or \\(y = \pm\frac{b}{a}x\\) for the equation of the asymptotes.
provide your answer below:
the asymptotes are \\(\square\\).

Explanation:

Step1: Identify $a$ and $b$ values

For the hyperbola $\frac{x^{2}}{9}-\frac{y^{2}}{36}=1$, we have $a^{2} = 9$ and $b^{2}=36$. So $a = 3$ and $b = 6$.

Step2: Determine the asymptote formula

The standard form of the asymptotes for a hyperbola of the form $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ is $y=\pm\frac{b}{a}x$.

Step3: Calculate the asymptotes

Substitute $a = 3$ and $b = 6$ into $y=\pm\frac{b}{a}x$. We get $y=\pm\frac{6}{3}x=\pm 2x$.

Answer:

$y = \pm 2x$