What is the asymptotes of 9y^2-100x^2=900 ?

The asymptotes of 9y^2-100x^2=900 is y=(10x)/3 ,\quad y=-(10x)/3

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asymptotes of 9y^2-100x^2=900

asymptotes

9 y^{2} - 100 x^{2} = 900

y = \frac{10 x}{3}, y = - \frac{10 x}{3}

Solution steps

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

Calculate Hyperbola properties

9 y^{2} - 100 x^{2} = 900 :

Up-down Hyperbola with

(h, k) = (0, 0), a = 10, b = 3

y = \frac{10}{3} (x - 0) + 0, y = - \frac{10}{3} (x - 0) + 0

Refine

y = \frac{10 x}{3}, y = - \frac{10 x}{3}

x^{2} - 3 y^{2} = 9

2 x^{2} - 2 y^{2} - 20 x + 16 y - 16 = 0

\frac{y ^{2}}{64} - \frac{x ^{2}}{16} = 1

y^{2} - x^{2} = \frac{9}{25}

25 y^{2} - 64 x^{2} = 1600

What is the asymptotes of 9y^2-100x^2=900 ?
The asymptotes of 9y^2-100x^2=900 is y=(10x)/3 ,\quad y=-(10x)/3