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{a}{b} (x - h) + k

Calculate Hyperbola properties

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

Up-down Hyperbola with

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

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

Refine

y = 2 x, y = - 2 x

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

\frac{y ^{2}}{16} - \frac{x ^{2}}{256} = 1

x^{2} - 4 y^{2} - 4 x + 24 y - 36 = 0

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

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