What is the asymptotes of 9x^2-4y^2-36x+72=0 ?

The asymptotes of 9x^2-4y^2-36x+72=0 is y= 3/2 (x-2),\quad y=-3/2 (x-2)

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asymptotes of 9x^2-4y^2-36x+72=0

asymptotes

9 x^{2} - 4 y^{2} - 36 x + 72 = 0

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

Solution steps

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

Calculate Hyperbola properties

9 x^{2} - 4 y^{2} - 36 x + 72 = 0 :

Up-down Hyperbola with

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

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

Refine

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

16 x^{2} - 25 y^{2} = 400

9 y^{2} - 5 x^{2} + 72 y + 30 x + 54 = 0

\frac{( y - 3 ) ^{2}}{9} - \frac{x ^{2}}{25} = 1

\frac{x ^{2}}{12} - \frac{y ^{2}}{16} = 1

9 y^{2} - 100 x^{2} = 900

What is the asymptotes of 9x^2-4y^2-36x+72=0 ?
The asymptotes of 9x^2-4y^2-36x+72=0 is y= 3/2 (x-2),\quad y=-3/2 (x-2)