What is the asymptotes of x^2-3y^2=9 ?

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

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asymptotes of x^2-3y^2=9

asymptotes

x^{2} - 3 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} - 3 y^{2} = 9 :

Right-left Hyperbola with

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

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

Refine

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

2 x^{2} - 2 y^{2} - 20 x + 16 y - 16 = 0

\frac{y ^{2}}{64} - \frac{x ^{2}}{16} = 1

y^{2} - x^{2} = \frac{9}{25}

25 y^{2} - 64 x^{2} = 1600

\frac{( y + 2 ) ^{2}}{4} - \frac{( x - 2 ) ^{2}}{9} = 1

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