What is the asymptotes of (y^2}{16}-\frac{x^2)/4 =1 ?

The asymptotes of (y^2}{16}-\frac{x^2)/4 =1 is y=2x,\quad y=-2x

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asymptotes of (y^2}{16}-\frac{x^2)/4 =1

asymptotes

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

y = 2 x, y = - 2 x

Solution steps

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

Calculate Hyperbola properties

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

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

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

\frac{( x - 2 ) ^{2}}{4} - \frac{( y + 3 ) ^{2}}{9} = 1

16 x^{2} - 9 y^{2} + 32 x + 72 y - 704 = 0

- 9 x^{2} + 16 y^{2} - 90 x + 128 y - 113 = 0

5 (y + 3)^{2} - 4 (x - 1)^{2} = 20

What is the asymptotes of (y^2}{16}-\frac{x^2)/4 =1 ?
The asymptotes of (y^2}{16}-\frac{x^2)/4 =1 is y=2x,\quad y=-2x