What is the asymptotes of 25y^2-16x^2-400=0 ?

The asymptotes of 25y^2-16x^2-400=0 is y=(4x)/5 ,\quad y=-(4x)/5

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asymptotes of 25y^2-16x^2-400=0

asymptotes

25 y^{2} - 16 x^{2} - 400 = 0

y = \frac{4 x}{5}, y = - \frac{4 x}{5}

Solution steps

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

Calculate Hyperbola properties

25 y^{2} - 16 x^{2} - 400 = 0 :

Up-down Hyperbola with

(h, k) = (0, 0), a = 4, b = 5

y = \frac{4}{5} (x - 0) + 0, y = - \frac{4}{5} (x - 0) + 0

Refine

y = \frac{4 x}{5}, y = - \frac{4 x}{5}

9 (y - 2)^{2} - 4 x^{2} = 36

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

4 x^{2} - 9 y^{2} - 36 = 0

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

- 4 x^{2} + 24 x + 16 y^{2} - 128 y + 156 = 0

What is the asymptotes of 25y^2-16x^2-400=0 ?
The asymptotes of 25y^2-16x^2-400=0 is y=(4x)/5 ,\quad y=-(4x)/5