What is the asymptotes of 0=-400/9 x^2+16y^2+400 ?

The asymptotes of 0=-400/9 x^2+16y^2+400 is y=(5x)/3 ,\quad y=-(5x)/3

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asymptotes of 0=-400/9 x^2+16y^2+400

asymptotes

0 = - \frac{400}{9} x^{2} + 16 y^{2} + 400

y = \frac{5 x}{3}, y = - \frac{5 x}{3}

Solution steps

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

Calculate Hyperbola properties

0 = - \frac{400}{9} x^{2} + 16 y^{2} + 400 :

Right-left Hyperbola with

(h, k) = (0, 0), a = 3, b = 5

y = \frac{5}{3} (x - 0) + 0, y = - \frac{5}{3} (x - 0) + 0

Refine

y = \frac{5 x}{3}, y = - \frac{5 x}{3}

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

9 x^{2} - 18 x - 16 y^{2} - 64 y = 199

\frac{x ^{2}}{4} - \frac{y ^{2}}{5} = 1

x^{2} - y^{2} + 4 x - 6 y = 6

9 x^{2} - 4 y^{2} + 36 x - 8 y - 40 = 0

What is the asymptotes of 0=-400/9 x^2+16y^2+400 ?
The asymptotes of 0=-400/9 x^2+16y^2+400 is y=(5x)/3 ,\quad y=-(5x)/3