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

\frac{( y + 2 ) ^{2}}{36} - x^{2} = 1

0 = - \frac{400}{9} x^{2} + 16 y^{2} + 400

\frac{x ^{2}}{16} - \frac{y ^{2}}{25} = 1

9 x^{2} - 18 x - 16 y^{2} - 64 y = 199

\frac{x ^{2}}{4} - \frac{y ^{2}}{5} = 1

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