What is the asymptotes of-9x^2+4y^2=36 ?

The asymptotes of-9x^2+4y^2=36 is y=(3x)/2 ,\quad y=-(3x)/2

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asymptotes of-9x^2+4y^2=36

asymptotes

- 9 x^{2} + 4 y^{2} = 36

y = \frac{3 x}{2}, y = - \frac{3 x}{2}

Solution steps

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

Calculate Hyperbola properties

- 9 x^{2} + 4 y^{2} = 36 :

Up-down Hyperbola with

(h, k) = (0, 0), a = 3, b = 2

y = \frac{3}{2} (x - 0) + 0, y = - \frac{3}{2} (x - 0) + 0

Refine

y = \frac{3 x}{2}, y = - \frac{3 x}{2}

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

16 y^{2} - x^{2} + 2 x + 64 y + 47 = 0

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

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

y^{2} - 4 x^{2} - 12 y - 16 x + 16 = 0

What is the asymptotes of-9x^2+4y^2=36 ?
The asymptotes of-9x^2+4y^2=36 is y=(3x)/2 ,\quad y=-(3x)/2