What is the asymptotes of (x^2)/4-(y^2)/4 =1 ?

The asymptotes of (x^2)/4-(y^2)/4 =1 is y=x,\quad y=-x

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asymptotes of (x^2)/4-(y^2)/4 =1

asymptotes

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

y = x, y = - x

Solution steps

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

Calculate Hyperbola properties

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

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

\frac{x ^{2}}{9} - \frac{y ^{2}}{4} = 1

\frac{y ^{2}}{36} - \frac{x ^{2}}{64} = 1

x = y - y^{2}

y^{2} - 8 x = 0

x^{2} - 2 x + y^{2} + 2 y = 7

What is the asymptotes of (x^2)/4-(y^2)/4 =1 ?
The asymptotes of (x^2)/4-(y^2)/4 =1 is y=x,\quad y=-x