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{a}{b} (x - h) + k

Calculate Hyperbola properties

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

Up-down Hyperbola with

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

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

Refine

y = 3 x, y = - 3 x

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

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

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

\frac{x ^{2}}{16} - \frac{y ^{2}}{25} = 1

9 x^{2} - 18 x - 16 y^{2} - 64 y = 199

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