What is the asymptotes of (y^2)/(25)-(x^2)/(81)=1 ?

The asymptotes of (y^2)/(25)-(x^2)/(81)=1 is y=(5x)/9 ,\quad y=-(5x)/9

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asymptotes of (y^2)/(25)-(x^2)/(81)=1

asymptotes

\frac{y ^{2}}{25} - \frac{x ^{2}}{81} = 1

y = \frac{5 x}{9}, y = - \frac{5 x}{9}

Solution steps

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

Calculate Hyperbola properties

\frac{y ^{2}}{25} - \frac{x ^{2}}{81} = 1 :

Up-down Hyperbola with

(h, k) = (0, 0), a = 5, b = 9

y = \frac{5}{9} (x - 0) + 0, y = - \frac{5}{9} (x - 0) + 0

Refine

y = \frac{5 x}{9}, y = - \frac{5 x}{9}

9 y^{2} - 25 x^{2} = 225

x^{2} - 4 y^{2} - 2 x + 16 y = 20

9 y^{2} - x^{2} + 2 x + 54 y + 62 = 0

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

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

What is the asymptotes of (y^2)/(25)-(x^2)/(81)=1 ?
The asymptotes of (y^2)/(25)-(x^2)/(81)=1 is y=(5x)/9 ,\quad y=-(5x)/9