What is the asymptotes of (y^2)/4-(x^2)/9 =1 ?

The asymptotes of (y^2)/4-(x^2)/9 =1 is y=(2x)/3 ,\quad y=-(2x)/3

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asymptotes of (y^2)/4-(x^2)/9 =1

asymptotes

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

Up-down Hyperbola with

(h, k) = (0, 0), a = 2, b = 3

y = \frac{2}{3} (x - 0) + 0, y = - \frac{2}{3} (x - 0) + 0

Refine

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

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

3 x^{2} - 15 y^{2} + 2 x - 3 y = 4

25 x^{2} - 9 y^{2} = 225

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

x^{2} - y^{2} - 4 x - 2 y - 13 = 0

What is the asymptotes of (y^2)/4-(x^2)/9 =1 ?
The asymptotes of (y^2)/4-(x^2)/9 =1 is y=(2x)/3 ,\quad y=-(2x)/3