What is the asymptotes of 9x^2-y^2+36x-12y=36 ?

The asymptotes of 9x^2-y^2+36x-12y=36 is y=3(x+2)-6,\quad y=-3(x+2)-6

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asymptotes of 9x^2-y^2+36x-12y=36

asymptotes

9 x^{2} - y^{2} + 36 x - 12 y = 36

y = 3 (x + 2) - 6, y = - 3 (x + 2) - 6

Solution steps

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

Calculate Hyperbola properties

9 x^{2} - y^{2} + 36 x - 12 y = 36 :

Right-left Hyperbola with

(h, k) = (- 2, - 6), a = 2, b = 6

y = \frac{6}{2} (x - (- 2)) + (- 6), y = - \frac{6}{2} (x - (- 2)) + (- 6)

Refine

y = 3 (x + 2) - 6, y = - 3 (x + 2) - 6

4 x^{2} - 24 x - 25 y^{2} + 250 y - 489 = 0

25 y^{2} - 81 x^{2} = 2025

6 x^{2} - 5 y^{2} - 24 x + 10 y - 11 = 0

x^{2} - 4 y^{2} + 2 x + 8 y - 7 = 0

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

What is the asymptotes of 9x^2-y^2+36x-12y=36 ?
The asymptotes of 9x^2-y^2+36x-12y=36 is y=3(x+2)-6,\quad y=-3(x+2)-6