What is the asymptotes of y^2-x^2=4 ?

The asymptotes of y^2-x^2=4 is y=x,\quad y=-x

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asymptotes of y^2-x^2=4

asymptotes

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

y = x, y = - x

Solution steps

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

Calculate Hyperbola properties

y^{2} - x^{2} = 4 :

Up-down Hyperbola with

(h, k) = (0, 0), a = 2, b = 2

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

Refine

y = x, y = - x

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

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

(x - 4)^{2} - (y - 5)^{2} = 15

\frac{x ^{2}}{81} - \frac{y ^{2}}{4} = 1

- 9 x^{2} - 32 y = - 16 y^{2} + 128

What is the asymptotes of y^2-x^2=4 ?
The asymptotes of y^2-x^2=4 is y=x,\quad y=-x