Find the asymptotes of the hyperbola $\frac{x^{2}}{81}-\frac{y^{2}}{25}=1$
A) $y=\frac{5}{9} x \text { and } y=-\frac{5}{9} x$
B) $y=\frac{5}{9} x+10.30 \text { and } y=-\frac{5}{9} x+10.30$
C) $y=\frac{9}{5} x \text { and } y=-\frac{9}{5} x$
D) y=2.06 x and y=-2.06 x

Question

Find the asymptotes of the hyperbola $\frac{x^{2}}{81}-\frac{y^{2}}{25}=1$
A) $y=\frac{5}{9} x \text { and } y=-\frac{5}{9} x$
B) $y=\frac{5}{9} x+10.30 \text { and } y=-\frac{5}{9} x+10.30$
C) $y=\frac{9}{5} x \text { and } y=-\frac{9}{5} x$
D)  y=2.06 x  and  y=-2.06 x

Quizplus · Accepted Answer

The asymptotes of a hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ are given by $y = \pm\frac{b}{a}x$. For this hyperbola, $a^2 = 81$ and $b^2 = 25$, so $a = 9$ and $b = 5$, leading to the asymptotes $y = \pm\frac{5}{9}x$.

Find the Asymptotes of the Hyperbola x281−y225=1\frac{x^{2}}{81}-\frac{y^{2}}{25}=181x2​−25y2​=1 A) y=59x and y=−59xy=\frac{5}{9} x \text { and } y=-\frac{5}{9} xy=95​x and y=−95​x

Find the Asymptotes of the Hyperbola $\frac{x^{2}}{81}-\frac{y^{2}}{25}=1$ A) $y=\frac{5}{9} x \text { and } y=-\frac{5}{9} x$