What is the asymptotes of 10x^2-25y^2=100 ?

The asymptotes of 10x^2-25y^2=100 is y=(sqrt(2)x)/(sqrt(5)),\quad y=-(sqrt(2)x)/(sqrt(5))

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asymptotes of 10x^2-25y^2=100

asymptotes

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

Solution steps

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

Calculate Hyperbola properties

10 x^{2} - 25 y^{2} = 100 :

Right-left Hyperbola with

(h, k) = (0, 0), a = 10, b = 2

y = \frac{2}{10} (x - 0) + 0, y = - \frac{2}{10} (x - 0) + 0

Refine

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

What is the asymptotes of 10x^2-25y^2=100 ?
The asymptotes of 10x^2-25y^2=100 is y=(sqrt(2)x)/(sqrt(5)),\quad y=-(sqrt(2)x)/(sqrt(5))