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

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

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

asymptotes

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

y = 2 x, y = - 2 x

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

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

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

Refine

y = 2 x, y = - 2 x

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

16 y^{2} - x^{2} + 2 x + 64 y - 1 = 0

5 x^{2} - 5 y^{2} + 20 x - 60 y = 185

9 y^{2} - 4 x^{2} - 36 y - 8 x = 4

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

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