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

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

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}

(x - 4)^{2} - (y + 1)^{2} = 25

- 9 x^{2} + 8 y^{2} + 36 x + 48 y = 36

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

5 x^{2} - 4 y^{2} - 20 x - 8 y = 4

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

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))