What is the asymptotes of 9x^2-y^2+36x-2y=46 ?

The asymptotes of 9x^2-y^2+36x-2y=46 is y=3(x+2)-1,\quad y=-3(x+2)-1

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asymptotes of 9x^2-y^2+36x-2y=46

asymptotes

9 x^{2} - y^{2} + 36 x - 2 y = 46

y = 3 (x + 2) - 1, y = - 3 (x + 2) - 1

Solution steps

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

Calculate Hyperbola properties

9 x^{2} - y^{2} + 36 x - 2 y = 46 :

Right-left Hyperbola with

(h, k) = (- 2, - 1), a = 3, b = 9

y = \frac{9}{3} (x - (- 2)) + (- 1), y = - \frac{9}{3} (x - (- 2)) + (- 1)

Refine

y = 3 (x + 2) - 1, y = - 3 (x + 2) - 1

x^{2} - y^{2} + 6 x = 41

\frac{( y ) ^{2}}{4} - \frac{( x ) ^{2}}{16} = 1

(x - 8)^{2} - (y + 6)^{2} = 1

4 x^{2} - 9 y^{2} - 18 y - 153 = 0

\frac{( x - 3 ) ^{2}}{4} - \frac{( y + 5 ) ^{2}}{9} = 1

What is the asymptotes of 9x^2-y^2+36x-2y=46 ?
The asymptotes of 9x^2-y^2+36x-2y=46 is y=3(x+2)-1,\quad y=-3(x+2)-1