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

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

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asymptotes of (x^2)/9-(y^2)/(64)=1

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

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

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} - 5 y^{2} = 7

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

\frac{x ^{2}}{4} - \frac{y ^{2}}{49} = 1

4 y^{2} - x^{2} = 900

9 (x - 1)^{2} - 16 (y + 2)^{2} = 144

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