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

Rewrite as

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

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}

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

9 y^{2} - 16 x^{2} = 144

(x - 5)^{2} - (y - 4)^{2} = 1

x^{2} - 4 y^{2} - 20 x - 64 y - 172 = 0

\frac{x ^{2}}{36} - \frac{y ^{2}}{4} = 1

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