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

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

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asymptotes of y^2-x^2=1

asymptotes

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

y = x, y = - x

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

(h, k) = (0, 0), a = 1, b = 1

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

Refine

y = x, y = - x

16 y^{2} - 32 y - 9 x^{2} - 18 x = 137

\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1

9 y^{2} - 36 x^{2} = 324

\frac{y ^{2}}{25} - \frac{x ^{2}}{81} = 1

9 y^{2} - 25 x^{2} = 225

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