What is the asymptotes of 9y^2-x^2+2x+54y+62=0 ?

The asymptotes of 9y^2-x^2+2x+54y+62=0 is y=(x-1)/3-3,\quad y=-(x-1)/3-3

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asymptotes of 9y^2-x^2+2x+54y+62=0

asymptotes

9 y^{2} - x^{2} + 2 x + 54 y + 62 = 0

y = \frac{x - 1}{3} - 3, y = - \frac{x - 1}{3} - 3

Solution steps

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

Calculate Hyperbola properties

9 y^{2} - x^{2} + 2 x + 54 y + 62 = 0 :

Up-down Hyperbola with

(h, k) = (1, - 3), a = 2, b = 32

y = \frac{2}{3 2} (x - 1) + (- 3), y = - \frac{2}{3 2} (x - 1) + (- 3)

Refine

y = \frac{x - 1}{3} - 3, y = - \frac{x - 1}{3} - 3

x^{2} - y^{2} < 1

\frac{( x + 5 ) ^{2}}{4} - \frac{y ^{2}}{4} = 1

\frac{x ^{2}}{25} - \frac{y ^{2}}{16} = 1

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

25 y^{2} - 16 x^{2} - 400 = 0

What is the asymptotes of 9y^2-x^2+2x+54y+62=0 ?
The asymptotes of 9y^2-x^2+2x+54y+62=0 is y=(x-1)/3-3,\quad y=-(x-1)/3-3