What is the asymptotes of x^2-4y^2=36 ?

The asymptotes of x^2-4y^2=36 is y= x/2 ,\quad y=-x/2

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asymptotes of x^2-4y^2=36

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

x^{2} - 4 y^{2} = 36 :

Right-left Hyperbola with

(h, k) = (0, 0), a = 6, b = 3

y = \frac{3}{6} (x - 0) + 0, y = - \frac{3}{6} (x - 0) + 0

Refine

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

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

x^{2} - 2 y^{2} + 3 x + 4 y = 2

\frac{1}{4} (y + 5)^{2} - \frac{1}{16} (x + 1)^{2} = 1

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

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

What is the asymptotes of x^2-4y^2=36 ?
The asymptotes of x^2-4y^2=36 is y= x/2 ,\quad y=-x/2