What is the asymptotes of x^2-4y^2=16 ?

The asymptotes of x^2-4y^2=16 is y= x/2 ,\quad y=-x/2

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asymptotes of x^2-4y^2=16

asymptotes

x^{2} - 4 y^{2} = 16

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} = 16 :

Right-left Hyperbola with

(h, k) = (0, 0), a = 4, b = 2

y = \frac{2}{4} (x - 0) + 0, y = - \frac{2}{4} (x - 0) + 0

Refine

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

x^{2} - 9 y^{2} - 4 x + 36 y - 41 = 0

\frac{y ^{2}}{64} - \frac{x ^{2}}{324} = 1

x^{2} - 16 y^{2} = 144

\frac{y ^{2}}{4} - \frac{x ^{2}}{16} = 1

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

What is the asymptotes of x^2-4y^2=16 ?
The asymptotes of x^2-4y^2=16 is y= x/2 ,\quad y=-x/2