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

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

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

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

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}

(x - 8)^{2} - (y + 6)^{2} = 1

4 x^{2} - 9 y^{2} - 18 y - 153 = 0

\frac{( x - 3 ) ^{2}}{4} - \frac{( y + 5 ) ^{2}}{9} = 1

4 x^{2} - y^{2} - 8 x + 6 y - 4 = 0

4 y^{2} - 25 x^{2} = 100

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