What is the asymptotes of (x/2)^2-(y/3)^2=1 ?

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

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asymptotes of (x/2)^2-(y/3)^2=1

asymptotes

(\frac{x}{2})^{2} - (\frac{y}{3})^{2} = 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})^{2} - (\frac{y}{3})^{2} = 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}

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

\frac{x ^{2}}{25} - \frac{y ^{2}}{64} = 1

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

y^{2} - 4 x^{2} + 4 x - 2 y - 4 = 0

16 y^{2} - x^{2} + 2 x + 64 y - 1 = 0

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