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

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

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

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

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

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

Refine

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

4 y^{2} - 5 x^{2} - 48 y - 10 x + 59 = 0

9 x^{2} - 4 y^{2} - 36 x + 72 = 0

16 x^{2} - 25 y^{2} = 400

9 y^{2} - 5 x^{2} + 72 y + 30 x + 54 = 0

\frac{( y - 3 ) ^{2}}{9} - \frac{x ^{2}}{25} = 1

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