What is the asymptotes of (y^2}{64}-\frac{x^2)/9 =1 ?

The asymptotes of (y^2}{64}-\frac{x^2)/9 =1 is y=(8x)/3 ,\quad y=-(8x)/3

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asymptotes of (y^2}{64}-\frac{x^2)/9 =1

asymptotes

\frac{y ^{2}}{64} - \frac{x ^{2}}{9} = 1

y = \frac{8 x}{3}, y = - \frac{8 x}{3}

Solution steps

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

Calculate Hyperbola properties

\frac{y ^{2}}{64} - \frac{x ^{2}}{9} = 1 :

Up-down Hyperbola with

(h, k) = (0, 0), a = 8, b = 3

y = \frac{8}{3} (x - 0) + 0, y = - \frac{8}{3} (x - 0) + 0

Refine

y = \frac{8 x}{3}, y = - \frac{8 x}{3}

x^{2} - y^{2} = 4

x^{2} - y^{2} + 8 x - 2 y + 14 = 0

\frac{( y - 2 ) ^{2}}{4} - \frac{( x + 3 ) ^{2}}{9} = 1

4 y^{2} - 2 x^{2} - 4 y - 8 x - 15 = 0

y^{2} = x^{2} - 4 x

What is the asymptotes of (y^2}{64}-\frac{x^2)/9 =1 ?
The asymptotes of (y^2}{64}-\frac{x^2)/9 =1 is y=(8x)/3 ,\quad y=-(8x)/3