What is the asymptotes of 9x^2-4y^2+72x+180=0 ?

The asymptotes of 9x^2-4y^2+72x+180=0 is y= 3/2 (x+4),\quad y=-3/2 (x+4)

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asymptotes of 9x^2-4y^2+72x+180=0

asymptotes

9 x^{2} - 4 y^{2} + 72 x + 180 = 0

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

Solution steps

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

Calculate Hyperbola properties

9 x^{2} - 4 y^{2} + 72 x + 180 = 0 :

Up-down Hyperbola with

(h, k) = (- 4, 0), a = 3, b = 2

y = \frac{3}{2} (x - (- 4)) + 0, y = - \frac{3}{2} (x - (- 4)) + 0

Refine

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

8 y^{2} - 32 x^{2} = 96

9 x^{2} - y^{2} + 36 x - 2 y = 46

x^{2} - y^{2} + 6 x = 41

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

(x - 8)^{2} - (y + 6)^{2} = 1

What is the asymptotes of 9x^2-4y^2+72x+180=0 ?
The asymptotes of 9x^2-4y^2+72x+180=0 is y= 3/2 (x+4),\quad y=-3/2 (x+4)