What is the asymptotes of y^2-(x^2)/9 =1 ?

The asymptotes of y^2-(x^2)/9 =1 is y= x/3 ,\quad y=-x/3

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asymptotes of y^2-(x^2)/9 =1

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

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

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

Refine

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

4 x^{2} - \frac{1}{2} y^{2} + 8 x + 2 y = 2

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

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

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

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

What is the asymptotes of y^2-(x^2)/9 =1 ?
The asymptotes of y^2-(x^2)/9 =1 is y= x/3 ,\quad y=-x/3