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

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

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asymptotes of x=x^2-(y^2)/9

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

(h, k) = (\frac{1}{2}, 0), a = \frac{1}{2}, b = \frac{3}{2}

y = \frac{\frac{3}{2}}{\frac{1}{2}} (x - \frac{1}{2}) + 0, y = - \frac{\frac{3}{2}}{\frac{1}{2}} (x - \frac{1}{2}) + 0

Refine

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

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

\frac{y ^{2}}{225} - \frac{x ^{2}}{81} = 1

9 + x^{2} - 3 y^{2} = 0

y^{2} - 4 x^{2} < 1

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

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