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

Calculate Hyperbola properties

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

Up-down Hyperbola with

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

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

Refine

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

\frac{( x + 9 ) ^{2}}{9} - \frac{( y - 8 ) ^{2}}{4} = 1

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

9 x^{2} - 16 y^{2} - 18 x + 64 y - 199 = 0

16 y^{2} - 25 x^{2} = 400

x^{2} - y^{2} = 100

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