What is the asymptotes of 9x^2-4y^2=36 ?

The asymptotes of 9x^2-4y^2=36 is y=(3x)/2 ,\quad y=-(3x)/2

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asymptotes of 9x^2-4y^2=36

asymptotes

9 x^{2} - 4 y^{2} = 36

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

Solution steps

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

Calculate Hyperbola properties

9 x^{2} - 4 y^{2} = 36 :

Right-left Hyperbola with

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

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

Refine

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

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

y^{2} - 4 y + 4 x = - 16

x^{2} + y^{2} + 6 x - 4 y - 23 = 0

y^{2} = - 8 x

16 y^{2} - 32 y - 9 x^{2} - 18 x = 137

What is the asymptotes of 9x^2-4y^2=36 ?
The asymptotes of 9x^2-4y^2=36 is y=(3x)/2 ,\quad y=-(3x)/2