What is the asymptotes of 5y^2-2x^2=9 ?

The asymptotes of 5y^2-2x^2=9 is y=(sqrt(2)x)/(sqrt(5)),\quad y=-(sqrt(2)x)/(sqrt(5))

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asymptotes of 5y^2-2x^2=9

asymptotes

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

y = \frac{2 x}{5}, y = - \frac{2 x}{5}

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

(h, k) = (0, 0), a = \frac{3}{5}, b = \frac{3}{2}

y = \frac{\frac{3}{5}}{\frac{3}{2}} (x - 0) + 0, y = - \frac{\frac{3}{5}}{\frac{3}{2}} (x - 0) + 0

Refine

y = \frac{2 x}{5}, y = - \frac{2 x}{5}

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

5 y^{2} - x^{2} = 25

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

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

9 x^{2} - 16 y^{2} + 36 x + 32 y - 124 = 0

What is the asymptotes of 5y^2-2x^2=9 ?
The asymptotes of 5y^2-2x^2=9 is y=(sqrt(2)x)/(sqrt(5)),\quad y=-(sqrt(2)x)/(sqrt(5))