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

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

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

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

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

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

Refine

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

9 y^{2} - 100 x^{2} = 900

x^{2} - 3 y^{2} = 9

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

\frac{y ^{2}}{64} - \frac{x ^{2}}{16} = 1

y^{2} - x^{2} = \frac{9}{25}

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