What is the asymptotes of 9y^2-16x^2=81 ?

The asymptotes of 9y^2-16x^2=81 is y=(4x)/3 ,\quad y=-(4x)/3

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asymptotes of 9y^2-16x^2=81

asymptotes

9 y^{2} - 16 x^{2} = 81

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} = 81 :

Up-down Hyperbola with

(h, k) = (0, 0), a = 3, b = \frac{9}{4}

y = \frac{3}{\frac{9}{4}} (x - 0) + 0, y = - \frac{3}{\frac{9}{4}} (x - 0) + 0

Refine

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

x = y^{2} - 2 y

y^{2} = - \frac{4}{5} (x - 2)

x^{2} - 4 y^{2} - 20 x - 64 y - 172 = 0

9 x^{2} + 4 y^{2} - 18 x + 8 y - 23 = 0

25 x^{2} + 4 y^{2} = 100

What is the asymptotes of 9y^2-16x^2=81 ?
The asymptotes of 9y^2-16x^2=81 is y=(4x)/3 ,\quad y=-(4x)/3