What is the asymptotes of (y^2)/(225)-(x^2)/(81)=1 ?

The asymptotes of (y^2)/(225)-(x^2)/(81)=1 is y=(5x)/3 ,\quad y=-(5x)/3

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asymptotes of (y^2)/(225)-(x^2)/(81)=1

asymptotes

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

y = \frac{5 x}{3}, y = - \frac{5 x}{3}

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

(h, k) = (0, 0), a = 15, b = 9

y = \frac{15}{9} (x - 0) + 0, y = - \frac{15}{9} (x - 0) + 0

Refine

y = \frac{5 x}{3}, y = - \frac{5 x}{3}

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

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

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

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

\frac{y ^{2}}{16} - \frac{x ^{2}}{256} = 1

What is the asymptotes of (y^2)/(225)-(x^2)/(81)=1 ?
The asymptotes of (y^2)/(225)-(x^2)/(81)=1 is y=(5x)/3 ,\quad y=-(5x)/3