What is the asymptotes of (y^2)/(16)-(x^2)/(36)=1 ?

The asymptotes of (y^2)/(16)-(x^2)/(36)=1 is y=(2x)/3 ,\quad y=-(2x)/3

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asymptotes of (y^2)/(16)-(x^2)/(36)=1

asymptotes

\frac{y ^{2}}{16} - \frac{x ^{2}}{36} = 1

y = \frac{2 x}{3}, y = - \frac{2 x}{3}

Solution steps

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

Calculate Hyperbola properties

\frac{y ^{2}}{16} - \frac{x ^{2}}{36} = 1 :

Up-down Hyperbola with

(h, k) = (0, 0), a = 4, b = 6

y = \frac{4}{6} (x - 0) + 0, y = - \frac{4}{6} (x - 0) + 0

Refine

y = \frac{2 x}{3}, y = - \frac{2 x}{3}

x^{2} - y^{2} - 4 x + 8 y - 21 = 0

\frac{x ^{2}}{7} - \frac{7 y ^{2}}{42} = 1

\frac{x ^{2}}{81} - \frac{y ^{2}}{9} = 1

\frac{y ^{2}}{4} - \frac{x ^{2}}{9} = 1

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

What is the asymptotes of (y^2)/(16)-(x^2)/(36)=1 ?
The asymptotes of (y^2)/(16)-(x^2)/(36)=1 is y=(2x)/3 ,\quad y=-(2x)/3