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

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

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

asymptotes

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

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} = 9 :

Right-left Hyperbola with

(h, k) = (0, 0), a = 3, b = 1

y = \frac{1}{3} (x - 0) + 0, y = - \frac{1}{3} (x - 0) + 0

Refine

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

- 9 x^{2} + 4 y^{2} - 36 x - 16 y - 164 = 0

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

x^{2} - y^{2} - 4 x + 8 y - 21 = 0

\frac{x ^{2}}{7} - \frac{7 y ^{2}}{42} = 1

\frac{x ^{2}}{81} - \frac{y ^{2}}{9} = 1

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