What is the asymptotes of 9x^2-36x-4y^2-24y-36=0 ?

The asymptotes of 9x^2-36x-4y^2-24y-36=0 is y= 3/2 (x-2)-3,\quad y=-3/2 (x-2)-3

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asymptotes of 9x^2-36x-4y^2-24y-36=0

asymptotes

9 x^{2} - 36 x - 4 y^{2} - 24 y - 36 = 0

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

Solution steps

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

Calculate Hyperbola properties

9 x^{2} - 36 x - 4 y^{2} - 24 y - 36 = 0 :

Right-left Hyperbola with

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

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

\frac{y ^{2}}{64} - \frac{x ^{2}}{81} = 1

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

2 x^{2} - 3 y^{2} = 6

6 x^{2} - 36 y^{2} = 2304

9 y^{2} - 16 x^{2} - 256 = 0

What is the asymptotes of 9x^2-36x-4y^2-24y-36=0 ?
The asymptotes of 9x^2-36x-4y^2-24y-36=0 is y= 3/2 (x-2)-3,\quad y=-3/2 (x-2)-3