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

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

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

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

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

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

Refine

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

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

9 x^{2} + 25 y^{2} - 36 x - 50 y + 60 = 0

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

25 x^{2} - 10 x - 200 y - 119 = 0

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

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