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

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

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asymptotes of x^2-y^2=4

asymptotes

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

y = x, y = - x

Solution steps

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

Calculate Hyperbola properties

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

Right-left 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

x^{2} - y^{2} + 8 x - 2 y + 14 = 0

\frac{( y - 2 ) ^{2}}{4} - \frac{( x + 3 ) ^{2}}{9} = 1

4 y^{2} - 2 x^{2} - 4 y - 8 x - 15 = 0

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

9 x^{2} - 16 y^{2} - 54 x + 64 y - 127 = 0

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