What is the asymptotes of 9+x^2-3y^2=0 ?

The asymptotes of 9+x^2-3y^2=0 is y= x/(sqrt(3)),\quad y=-x/(sqrt(3))

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asymptotes of 9+x^2-3y^2=0

asymptotes

9 + x^{2} - 3 y^{2} = 0

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

Solution steps

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

Calculate Hyperbola properties

9 + x^{2} - 3 y^{2} = 0 :

Up-down 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}

y^{2} - 4 x^{2} < 1

4 x^{2} - y^{2} = - 16

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

\frac{y ^{2}}{16} - \frac{x ^{2}}{256} = 1

x^{2} - 4 y^{2} - 4 x + 24 y - 36 = 0

What is the asymptotes of 9+x^2-3y^2=0 ?
The asymptotes of 9+x^2-3y^2=0 is y= x/(sqrt(3)),\quad y=-x/(sqrt(3))