What is the asymptotes of ((y)^2)/(12)-(x^2)/(16)=1 ?

The asymptotes of ((y)^2)/(12)-(x^2)/(16)=1 is y=(sqrt(3)x)/2 ,\quad y=-(sqrt(3)x)/2

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asymptotes of ((y)^2)/(12)-(x^2)/(16)=1

asymptotes

\frac{( y ) ^{2}}{12} - \frac{x ^{2}}{16} = 1

y = \frac{3 x}{2}, y = - \frac{3 x}{2}

Solution steps

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

Calculate Hyperbola properties

\frac{y ^{2}}{12} - \frac{x ^{2}}{16} = 1 :

Up-down Hyperbola with

(h, k) = (0, 0), a = 23, b = 4

y = \frac{2 3}{4} (x - 0) + 0, y = - \frac{2 3}{4} (x - 0) + 0

Refine

y = \frac{3 x}{2}, y = - \frac{3 x}{2}

9 x^{2} - 18 x - 24 y - 63 = 4 y^{2}

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

3 x^{2} - 8 y^{2} + 12 x + 16 y + 20 = 0

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

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

What is the asymptotes of ((y)^2)/(12)-(x^2)/(16)=1 ?
The asymptotes of ((y)^2)/(12)-(x^2)/(16)=1 is y=(sqrt(3)x)/2 ,\quad y=-(sqrt(3)x)/2