What is the asymptotes of x^2-y^2-8=0 ?

The asymptotes of x^2-y^2-8=0 is y=x,\quad y=-x

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asymptotes of x^2-y^2-8=0

asymptotes

x^{2} - y^{2} - 8 = 0

y = x, y = - x

Solution steps

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

Calculate Hyperbola properties

x^{2} - y^{2} - 8 = 0 :

Right-left Hyperbola with

(h, k) = (0, 0), a = 22, b = 22

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

Refine

y = x, y = - x

\frac{x ^{2}}{64} - \frac{y ^{2}}{81} = 1

\frac{x ^{2}}{5} - \frac{y ^{2}}{12} = 1

9 x^{2} = 4 y^{2} - 12

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

4 x^{2} - y^{2} + 16 x + 6 y = 9

What is the asymptotes of x^2-y^2-8=0 ?
The asymptotes of x^2-y^2-8=0 is y=x,\quad y=-x