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

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

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

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

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

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

Refine

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

x^{2} - 9 y^{2} = 144

9 x^{2} - 16 y^{2} + 36 x + 32 y - 124 = 0

4 x^{2} - 25 y^{2} + 16 x + 50 y - 109 = 0

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

\frac{x ^{2}}{4} - \frac{y ^{2}}{36} = 1

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