What is the asymptotes of-9x^2-32y=-16y^2+128 ?

The asymptotes of-9x^2-32y=-16y^2+128 is y=(3x)/4+1,\quad y=-(3x)/4+1

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asymptotes of-9x^2-32y=-16y^2+128

asymptotes

- 9 x^{2} - 32 y = - 16 y^{2} + 128

y = \frac{3 x}{4} + 1, y = - \frac{3 x}{4} + 1

Solution steps

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

Calculate Hyperbola properties

- 9 x^{2} - 32 y = - 16 y^{2} + 128 :

Up-down Hyperbola with

(h, k) = (0, 1), a = 3, b = 4

y = \frac{3}{4} (x - 0) + 1, y = - \frac{3}{4} (x - 0) + 1

Refine

y = \frac{3 x}{4} + 1, y = - \frac{3 x}{4} + 1

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

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

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

\frac{x ^{2}}{5} - \frac{y ^{2}}{12} = 1

9 x^{2} = 4 y^{2} - 12

What is the asymptotes of-9x^2-32y=-16y^2+128 ?
The asymptotes of-9x^2-32y=-16y^2+128 is y=(3x)/4+1,\quad y=-(3x)/4+1