What is the asymptotes of 9x^2-4y^2+36x-8y-40=0 ?

The asymptotes of 9x^2-4y^2+36x-8y-40=0 is y=(3(x+2))/2-1,\quad y=-(3(x+2))/2-1

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asymptotes of 9x^2-4y^2+36x-8y-40=0

asymptotes

9 x^{2} - 4 y^{2} + 36 x - 8 y - 40 = 0

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

Solution steps

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

Calculate Hyperbola properties

9 x^{2} - 4 y^{2} + 36 x - 8 y - 40 = 0 :

Right-left Hyperbola with

(h, k) = (- 2, - 1), a = 22, b = 32

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

Refine

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

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

4 x^{2} - y^{2} = 2

4 x^{2} - y^{2} = 4

4 x^{2} - \frac{1}{2} y^{2} + 8 x + 2 y - 2 = 0

\frac{x ^{2}}{10} - \frac{y ^{2}}{90} = 1

What is the asymptotes of 9x^2-4y^2+36x-8y-40=0 ?
The asymptotes of 9x^2-4y^2+36x-8y-40=0 is y=(3(x+2))/2-1,\quad y=-(3(x+2))/2-1