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

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

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

asymptotes

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

y = 2 x, y = - 2 x

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

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

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

Refine

y = 2 x, y = - 2 x

x^{2} + y^{2} - 4 x - 4 y = 0

x^{2} = - 4 y

\frac{x ^{2}}{25} + \frac{y ^{2}}{9} = 1

x = y^{2} - 4

\frac{( x - 5 ) ^{2}}{4} + \frac{( y + 3 ) ^{2}}{16} = 1

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