What is the asymptotes of 9x^2-36y^2=324 ?

The asymptotes of 9x^2-36y^2=324 is y= x/2 ,\quad y=-x/2

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asymptotes of 9x^2-36y^2=324

asymptotes

9 x^{2} - 36 y^{2} = 324

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

Solution steps

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

Calculate Hyperbola properties

9 x^{2} - 36 y^{2} = 324 :

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}

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

4 x^{2} - 8 x - 9 y^{2} - 72 y + 112 = 0

9 x^{2} - 25 y^{2} = 225

\frac{x ^{2}}{9} - \frac{y ^{2}}{25} = 1

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

What is the asymptotes of 9x^2-36y^2=324 ?
The asymptotes of 9x^2-36y^2=324 is y= x/2 ,\quad y=-x/2