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

The asymptotes of y^2-9x^2=9 is y=3x,\quad y=-3x

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asymptotes of y^2-9x^2=9

asymptotes

y^{2} - 9 x^{2} = 9

y = 3 x, y = - 3 x

Solution steps

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

Calculate Hyperbola properties

y^{2} - 9 x^{2} = 9 :

Up-down Hyperbola with

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

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

Refine

y = 3 x, y = - 3 x

x^{2} - 2 y^{2} + 3 x + 4 y = 2

\frac{1}{4} (y + 5)^{2} - \frac{1}{16} (x + 1)^{2} = 1

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

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

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

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