What is the asymptotes of (x^2)/9-(y^2)/4 =1 ?

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

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asymptotes of (x^2)/9-(y^2)/4 =1

asymptotes

\frac{x ^{2}}{9} - \frac{y ^{2}}{4} = 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}}{9} - \frac{y ^{2}}{4} = 1 :

Right-left Hyperbola with

(h, k) = (0, 0), a = 3, b = 2

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

Refine

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

f (x) = - 3 x^{2} + 12 x - 8

9 x^{2} + y^{2} = 9

y = x^{2}

x^{2} = 2 y

x = y^{2}

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