What is the asymptotes of (x^2}{36}-\frac{y^2)/9 =1 ?

The asymptotes of (x^2}{36}-\frac{y^2)/9 =1 is y= x/2 ,\quad y=-x/2

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asymptotes of (x^2}{36}-\frac{y^2)/9 =1

asymptotes

\frac{x ^{2}}{36} - \frac{y ^{2}}{9} = 1

y = \frac{x}{2}, y = - \frac{x}{2}

Solution steps

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

Calculate Hyperbola properties

\frac{x ^{2}}{36} - \frac{y ^{2}}{9} = 1 :

Right-left Hyperbola with

(h, k) = (0, 0), a = 6, b = 3

y = \frac{3}{6} (x - 0) + 0, y = - \frac{3}{6} (x - 0) + 0

Refine

y = \frac{x}{2}, y = - \frac{x}{2}

x^{2} = 8 y

y^{2} = 32 x

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

3 x^{2} + y^{2} + 18 x - 2 y - 8 = 0

x^{2} = 12 y

What is the asymptotes of (x^2}{36}-\frac{y^2)/9 =1 ?
The asymptotes of (x^2}{36}-\frac{y^2)/9 =1 is y= x/2 ,\quad y=-x/2