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

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

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

asymptotes

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

y = 3 x + 3, y = - 3 x + 3

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

(h, k) = (0, 3), a = 1, b = 3

y = \frac{3}{1} (x - 0) + 3, y = - \frac{3}{1} (x - 0) + 3

Refine

y = 3 x + 3, y = - 3 x + 3

4 x^{2} - y^{2} - 24 x - 6 y + 23 = 0

y^{2} - x^{2} = \frac{4}{25}

3 x^{2} - y^{2} + 6 x - 2 y = 10

\frac{( x - 1 ) ^{2}}{9} - \frac{( y + 6 ) ^{2}}{4} = 1

\frac{x ^{2}}{16} - \frac{y ^{2}}{20} = 1

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