What is the asymptotes of (x^2}{81}-\frac{y^2)/4 =1 ?

The asymptotes of (x^2}{81}-\frac{y^2)/4 =1 is y=(2x)/9 ,\quad y=-(2x)/9

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asymptotes of (x^2}{81}-\frac{y^2)/4 =1

asymptotes

\frac{x ^{2}}{81} - \frac{y ^{2}}{4} = 1

y = \frac{2 x}{9}, y = - \frac{2 x}{9}

Solution steps

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

Calculate Hyperbola properties

\frac{x ^{2}}{81} - \frac{y ^{2}}{4} = 1 :

Right-left Hyperbola with

(h, k) = (0, 0), a = 9, b = 2

y = \frac{2}{9} (x - 0) + 0, y = - \frac{2}{9} (x - 0) + 0

Refine

y = \frac{2 x}{9}, y = - \frac{2 x}{9}

- 9 x^{2} - 32 y = - 16 y^{2} + 128

y^{2} - x^{2} = 81

x^{2} - y^{2} - 8 = 0

\frac{x ^{2}}{64} - \frac{y ^{2}}{81} = 1

\frac{x ^{2}}{5} - \frac{y ^{2}}{12} = 1

What is the asymptotes of (x^2}{81}-\frac{y^2)/4 =1 ?
The asymptotes of (x^2}{81}-\frac{y^2)/4 =1 is y=(2x)/9 ,\quad y=-(2x)/9