What is the asymptotes of (y^2)/(64)-(x^2)/(81)=1 ?

The asymptotes of (y^2)/(64)-(x^2)/(81)=1 is y=(8x)/9 ,\quad y=-(8x)/9

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asymptotes of (y^2)/(64)-(x^2)/(81)=1

asymptotes

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

y = \frac{8 x}{9}, y = - \frac{8 x}{9}

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

(h, k) = (0, 0), a = 8, b = 9

y = \frac{8}{9} (x - 0) + 0, y = - \frac{8}{9} (x - 0) + 0

Refine

y = \frac{8 x}{9}, y = - \frac{8 x}{9}

\frac{( y - 2 ) ^{2}}{9} - (x + 2)^{2} = 1

2 x^{2} - 3 y^{2} = 6

6 x^{2} - 36 y^{2} = 2304

9 y^{2} - 16 x^{2} - 256 = 0

- 9 x^{2} + y^{2} = 36

What is the asymptotes of (y^2)/(64)-(x^2)/(81)=1 ?
The asymptotes of (y^2)/(64)-(x^2)/(81)=1 is y=(8x)/9 ,\quad y=-(8x)/9