What is the asymptotes of 9x^2-4y^2-72x=0 ?

The asymptotes of 9x^2-4y^2-72x=0 is y=(3(x-4))/2 ,\quad y=-(3(x-4))/2

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asymptotes of 9x^2-4y^2-72x=0

asymptotes

9 x^{2} - 4 y^{2} - 72 x = 0

y = \frac{3 ( x - 4 )}{2}, y = - \frac{3 ( x - 4 )}{2}

Solution steps

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

Calculate Hyperbola properties

9 x^{2} - 4 y^{2} - 72 x = 0 :

Right-left Hyperbola with

(h, k) = (4, 0), a = 4, b = 6

y = \frac{6}{4} (x - 4) + 0, y = - \frac{6}{4} (x - 4) + 0

Refine

y = \frac{3 ( x - 4 )}{2}, y = - \frac{3 ( x - 4 )}{2}

y = 2 x^{2}

\frac{x ^{2}}{7} + \frac{y ^{2}}{16} = 1

x^{2} = y + 2

x^{2} = 24 y

2 x^{2} + 16 y = 0

What is the asymptotes of 9x^2-4y^2-72x=0 ?
The asymptotes of 9x^2-4y^2-72x=0 is y=(3(x-4))/2 ,\quad y=-(3(x-4))/2