What is the asymptotes of 9y^2-5x^2+72y+30x+54=0 ?

The asymptotes of 9y^2-5x^2+72y+30x+54=0 is y=(sqrt(5))/3 (x-3)-4,\quad y=-(sqrt(5))/3 (x-3)-4

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asymptotes of 9y^2-5x^2+72y+30x+54=0

asymptotes

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

y = \frac{5}{3} (x - 3) - 4, y = - \frac{5}{3} (x - 3) - 4

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

(h, k) = (3, - 4), a = 5, b = 3

y = \frac{5}{3} (x - 3) + (- 4), y = - \frac{5}{3} (x - 3) + (- 4)

\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

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

2 x^{2} - 2 y^{2} - 20 x + 16 y - 16 = 0

What is the asymptotes of 9y^2-5x^2+72y+30x+54=0 ?
The asymptotes of 9y^2-5x^2+72y+30x+54=0 is y=(sqrt(5))/3 (x-3)-4,\quad y=-(sqrt(5))/3 (x-3)-4