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

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

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

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

(h, k) = (0, 0), a = 6, b = 2

y = \frac{2}{6} (x - 0) + 0, y = - \frac{2}{6} (x - 0) + 0

Refine

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

(x - 4)^{2} - (y - 5)^{2} = 15

\frac{x ^{2}}{81} - \frac{y ^{2}}{4} = 1

- 9 x^{2} - 32 y = - 16 y^{2} + 128

y^{2} - x^{2} = 81

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

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