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

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

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asymptotes of (x^2)/4-(y^2)/(16)=1

asymptotes

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

y = 2 x, y = - 2 x

Solution steps

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

Calculate Hyperbola properties

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

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

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

9 x^{2} - 4 y^{2} + 72 x + 180 = 0

8 y^{2} - 32 x^{2} = 96

9 x^{2} - y^{2} + 36 x - 2 y = 46

x^{2} - y^{2} + 6 x = 41

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