What is the asymptotes of 9x^2-y^2-36x-6y+18=0 ?

The asymptotes of 9x^2-y^2-36x-6y+18=0 is y=3(x-2)-3,\quad y=-3(x-2)-3

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asymptotes of 9x^2-y^2-36x-6y+18=0

asymptotes

9 x^{2} - y^{2} - 36 x - 6 y + 18 = 0

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

Solution steps

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

Calculate Hyperbola properties

9 x^{2} - y^{2} - 36 x - 6 y + 18 = 0 :

Right-left Hyperbola with

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

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

Refine

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

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

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

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

y^{2} - x^{2} = 1

16 y^{2} - 32 y - 9 x^{2} - 18 x = 137

What is the asymptotes of 9x^2-y^2-36x-6y+18=0 ?
The asymptotes of 9x^2-y^2-36x-6y+18=0 is y=3(x-2)-3,\quad y=-3(x-2)-3