What is the asymptotes of y^2-x^2= 1/25 ?

The asymptotes of y^2-x^2= 1/25 is y=x,\quad y=-x

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asymptotes of y^2-x^2= 1/25

asymptotes

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

y = x, y = - x

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

(h, k) = (0, 0), a = \frac{1}{5}, b = \frac{1}{5}

y = \frac{\frac{1}{5}}{\frac{1}{5}} (x - 0) + 0, y = - \frac{\frac{1}{5}}{\frac{1}{5}} (x - 0) + 0

Refine

y = x, y = - x

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

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

\frac{x ^{2}}{49} - y^{2} = 1

+ \frac{x ^{2}}{16} - \frac{y ^{2}}{9} = 1

9 x^{2} - 36 x - 4 y^{2} - 24 y - 36 = 0

What is the asymptotes of y^2-x^2= 1/25 ?
The asymptotes of y^2-x^2= 1/25 is y=x,\quad y=-x