What is the asymptotes of 9x^2-y^2-54x-2y+71=0 ?

The asymptotes of 9x^2-y^2-54x-2y+71=0 is y=3(x-3)-1,\quad y=-3(x-3)-1

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asymptotes of 9x^2-y^2-54x-2y+71=0

asymptotes

9 x^{2} - y^{2} - 54 x - 2 y + 71 = 0

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

Solution steps

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

Calculate Hyperbola properties

9 x^{2} - y^{2} - 54 x - 2 y + 71 = 0 :

Right-left Hyperbola with

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

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

Refine

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

4 y^{2} - 9 x^{2} + 16 y + 18 x = 29

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

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

\frac{( x + 2 ) ^{2}}{36} - y^{2} = 1

y^{2} - x^{2} = 16

What is the asymptotes of 9x^2-y^2-54x-2y+71=0 ?
The asymptotes of 9x^2-y^2-54x-2y+71=0 is y=3(x-3)-1,\quad y=-3(x-3)-1