What is the asymptotes of 9y^2-16x^2-256=0 ?

The asymptotes of 9y^2-16x^2-256=0 is y=(4x)/3 ,\quad y=-(4x)/3

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asymptotes of 9y^2-16x^2-256=0

asymptotes

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

y = \frac{4 x}{3}, y = - \frac{4 x}{3}

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

(h, k) = (0, 0), a = \frac{16}{3}, b = 4

y = \frac{\frac{16}{3}}{4} (x - 0) + 0, y = - \frac{\frac{16}{3}}{4} (x - 0) + 0

Refine

y = \frac{4 x}{3}, y = - \frac{4 x}{3}

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

y^{2} = x^{2} - 1

\frac{( y + 2 ) ^{2}}{36} - x^{2} = 1

0 = - \frac{400}{9} x^{2} + 16 y^{2} + 400

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

What is the asymptotes of 9y^2-16x^2-256=0 ?
The asymptotes of 9y^2-16x^2-256=0 is y=(4x)/3 ,\quad y=-(4x)/3