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

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

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

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

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

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

Refine

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

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

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

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

- x^{2} + y^{2} = 1

5 y^{2} - x^{2} = 25

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