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

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

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

asymptotes

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

y = \frac{x}{4}, y = - \frac{x}{4}

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

(h, k) = (0, 0), a = 4, b = 1

y = \frac{1}{4} (x - 0) + 0, y = - \frac{1}{4} (x - 0) + 0

Refine

y = \frac{x}{4}, y = - \frac{x}{4}

- \frac{y ^{2}}{1} + \frac{x ^{2}}{49} = 1

\frac{x ^{2}}{9} - \frac{y ^{2}}{49} = 1

\frac{( x - 3 ) ^{2}}{49} - \frac{( y + 5 ) ^{2}}{25} = 1

25 x^{2} - 9 y^{2} = 225

\frac{( y - 3 ) ^{2}}{8 ^{2}} - \frac{( x - 2 ) ^{2}}{8 ^{2}} = 1

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