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

The asymptotes of 9x^2-y^2=36 is y=3x,\quad y=-3x

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

asymptotes

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

y = 3 x, y = - 3 x

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

(h, k) = (0, 0), a = 2, b = 6

y = \frac{6}{2} (x - 0) + 0, y = - \frac{6}{2} (x - 0) + 0

Refine

y = 3 x, y = - 3 x

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

\frac{y ^{2}}{4} - \frac{x ^{2}}{25} = 1

What is the asymptotes of 9x^2-y^2=36 ?
The asymptotes of 9x^2-y^2=36 is y=3x,\quad y=-3x