What is the asymptotes of 5y^2-x^2=25 ?

The asymptotes of 5y^2-x^2=25 is y= x/(sqrt(5)),\quad y=-x/(sqrt(5))

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asymptotes of 5y^2-x^2=25

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

(h, k) = (0, 0), a = 5, b = 5

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

Refine

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

\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

4 x^{2} - 25 y^{2} + 16 x + 50 y - 109 = 0

(\frac{x}{2})^{2} - (\frac{y}{3})^{2} = 1

What is the asymptotes of 5y^2-x^2=25 ?
The asymptotes of 5y^2-x^2=25 is y= x/(sqrt(5)),\quad y=-x/(sqrt(5))