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

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

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

asymptotes

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

y = 3 x, y = - 3 x

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

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

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

Refine

y = 3 x, y = - 3 x

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

- 16 x^{2} + 25 y^{2} - 64 x - 150 y - 239 = 0

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