What is the asymptotes of (x^2)/9-(y^2)/(16)=1 ?

The asymptotes of (x^2)/9-(y^2)/(16)=1 is y=(4x)/3 ,\quad y=-(4x)/3

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asymptotes of (x^2)/9-(y^2)/(16)=1

asymptotes

\frac{x ^{2}}{9} - \frac{y ^{2}}{16} = 1

y = \frac{4 x}{3}, y = - \frac{4 x}{3}

Solution steps

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

Calculate Hyperbola properties

\frac{x ^{2}}{9} - \frac{y ^{2}}{16} = 1 :

Right-left Hyperbola with

(h, k) = (0, 0), a = 3, b = 4

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

Refine

y = \frac{4 x}{3}, y = - \frac{4 x}{3}

\frac{x ^{2}}{9} + \frac{y ^{2}}{25} = 1

9 x^{2} - y^{2} - 36 x - 6 y + 18 = 0

\frac{x ^{2}}{25} + \frac{y ^{2}}{49} = 1

\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1

\frac{x ^{2}}{36} + \frac{y ^{2}}{4} = 1

What is the asymptotes of (x^2)/9-(y^2)/(16)=1 ?
The asymptotes of (x^2)/9-(y^2)/(16)=1 is y=(4x)/3 ,\quad y=-(4x)/3