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

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

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

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

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

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} - 5 x^{2} + 72 y + 30 x + 54 = 0

\frac{( y - 3 ) ^{2}}{9} - \frac{x ^{2}}{25} = 1

\frac{x ^{2}}{12} - \frac{y ^{2}}{16} = 1

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

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

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