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

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

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asymptotes of x^2-4y^2=4

asymptotes

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

y = \frac{x}{2}, y = - \frac{x}{2}

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

(h, k) = (0, 0), a = 2, b = 1

y = \frac{1}{2} (x - 0) + 0, y = - \frac{1}{2} (x - 0) + 0

Refine

y = \frac{x}{2}, y = - \frac{x}{2}

4 x^{2} - 9 y^{2} - 36 = 0

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

- 4 x^{2} + 24 x + 16 y^{2} - 128 y + 156 = 0

\frac{y ^{2}}{64} - \frac{x ^{2}}{9} = 1

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

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