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

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

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

asymptotes

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

y = 2 x, y = - 2 x

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

(h, k) = (0, 0), a = \frac{1}{2}, b = 2

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

Refine

y = 2 x, y = - 2 x

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

4 x^{2} - \frac{1}{2} y^{2} + 8 x + 2 y - 2 = 0

\frac{x ^{2}}{10} - \frac{y ^{2}}{90} = 1

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

x^{2} - 3 y^{2} - 2 x - 6 y + 7 = 0

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