What is the asymptotes of 4x^2-9y^2-36=0 ?

The asymptotes of 4x^2-9y^2-36=0 is y=(2x)/3 ,\quad y=-(2x)/3

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asymptotes of 4x^2-9y^2-36=0

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

4 x^{2} - 9 y^{2} - 36 = 0 :

Right-left Hyperbola with

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

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

- 4 x^{2} + 24 x + 16 y^{2} - 128 y + 156 = 0

\frac{y ^{2}}{64} - \frac{x ^{2}}{9} = 1

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

x^{2} - y^{2} + 8 x - 2 y + 14 = 0

What is the asymptotes of 4x^2-9y^2-36=0 ?
The asymptotes of 4x^2-9y^2-36=0 is y=(2x)/3 ,\quad y=-(2x)/3