What is the asymptotes of (x^2}{81}-\frac{y^2)/9 =1 ?

The asymptotes of (x^2}{81}-\frac{y^2)/9 =1 is y= x/3 ,\quad y=-x/3

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asymptotes of (x^2}{81}-\frac{y^2)/9 =1

asymptotes

\frac{x ^{2}}{81} - \frac{y ^{2}}{9} = 1

y = \frac{x}{3}, y = - \frac{x}{3}

Solution steps

y = \pm \frac{b}{a} (x - h) + k

Calculate Hyperbola properties

\frac{x ^{2}}{81} - \frac{y ^{2}}{9} = 1 :

Right-left Hyperbola with

(h, k) = (0, 0), a = 9, b = 3

y = \frac{3}{9} (x - 0) + 0, y = - \frac{3}{9} (x - 0) + 0

Refine

y = \frac{x}{3}, y = - \frac{x}{3}

\frac{y ^{2}}{4} - \frac{x ^{2}}{9} = 1

\frac{y ^{2}}{25} - \frac{x ^{2}}{16} = 1

3 x^{2} - 15 y^{2} + 2 x - 3 y = 4

25 x^{2} - 9 y^{2} = 225

\frac{y ^{2}}{36} - \frac{x ^{2}}{16} = 1

What is the asymptotes of (x^2}{81}-\frac{y^2)/9 =1 ?
The asymptotes of (x^2}{81}-\frac{y^2)/9 =1 is y= x/3 ,\quad y=-x/3