What is the asymptotes of 6x^2-36y^2=2304 ?

The asymptotes of 6x^2-36y^2=2304 is y= x/(sqrt(6)),\quad y=-x/(sqrt(6))

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asymptotes of 6x^2-36y^2=2304

asymptotes

6 x^{2} - 36 y^{2} = 2304

y = \frac{x}{6}, y = - \frac{x}{6}

Solution steps

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

Calculate Hyperbola properties

6 x^{2} - 36 y^{2} = 2304 :

Right-left Hyperbola with

(h, k) = (0, 0), a = 86, b = 8

y = \frac{8}{8 6} (x - 0) + 0, y = - \frac{8}{8 6} (x - 0) + 0

Refine

y = \frac{x}{6}, y = - \frac{x}{6}

9 y^{2} - 16 x^{2} - 256 = 0

- 9 x^{2} + y^{2} = 36

y^{2} = x^{2} - 1

\frac{( y + 2 ) ^{2}}{36} - x^{2} = 1

0 = - \frac{400}{9} x^{2} + 16 y^{2} + 400

What is the asymptotes of 6x^2-36y^2=2304 ?
The asymptotes of 6x^2-36y^2=2304 is y= x/(sqrt(6)),\quad y=-x/(sqrt(6))