What is the asymptotes of x^2-4y^2-8=0 ?

The asymptotes of x^2-4y^2-8=0 is y= x/2 ,\quad y=-x/2

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asymptotes of x^2-4y^2-8=0

asymptotes

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

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} - 8 = 0 :

Right-left Hyperbola with

(h, k) = (0, 0), a = 22, b = 2

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

Refine

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

4 y^{2} - x^{2} + 40 y - 4 x + 60 = 0

16 x^{2} - y^{2} = 256

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

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

- 9 x^{2} + 16 y^{2} - 90 x + 32 y - 353 = 0

What is the asymptotes of x^2-4y^2-8=0 ?
The asymptotes of x^2-4y^2-8=0 is y= x/2 ,\quad y=-x/2