What is the asymptotes of 9y^2-4x^2-36y-8x=4 ?

The asymptotes of 9y^2-4x^2-36y-8x=4 is y= 2/3 (x+1)+2,\quad y=-2/3 (x+1)+2

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asymptotes of 9y^2-4x^2-36y-8x=4

asymptotes

9 y^{2} - 4 x^{2} - 36 y - 8 x = 4

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

Solution steps

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

Calculate Hyperbola properties

9 y^{2} - 4 x^{2} - 36 y - 8 x = 4 :

Up-down Hyperbola with

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

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

Refine

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

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

\frac{x ^{2}}{16} - \frac{y ^{2}}{64} = 1

\frac{y ^{2}}{49} - \frac{x ^{2}}{36} = 1

\frac{x ^{2}}{49} - \frac{y ^{2}}{36} = 1

\frac{( y - 5 ) ^{2}}{16} - (x + 5)^{2} = 1

What is the asymptotes of 9y^2-4x^2-36y-8x=4 ?
The asymptotes of 9y^2-4x^2-36y-8x=4 is y= 2/3 (x+1)+2,\quad y=-2/3 (x+1)+2