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}

8 x^{2} - 2 y^{2} = 16

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

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

\frac{y ^{2}}{225} - \frac{x ^{2}}{81} = 1

9 + x^{2} - 3 y^{2} = 0

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