What is the asymptotes of 8x^2-2y^2=16 ?

The asymptotes of 8x^2-2y^2=16 is y=2x,\quad y=-2x

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asymptotes of 8x^2-2y^2=16

asymptotes

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

y = 2 x, y = - 2 x

Solution steps

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

Calculate Hyperbola properties

8 x^{2} - 2 y^{2} = 16 :

Right-left Hyperbola with

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

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

Refine

y = 2 x, y = - 2 x

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

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

\frac{y ^{2}}{225} - \frac{x ^{2}}{81} = 1

9 + x^{2} - 3 y^{2} = 0

y^{2} - 4 x^{2} < 1

What is the asymptotes of 8x^2-2y^2=16 ?
The asymptotes of 8x^2-2y^2=16 is y=2x,\quad y=-2x