What is the asymptotes of (x^2)/9-(y^2)/(25)=1 ?

The asymptotes of (x^2)/9-(y^2)/(25)=1 is y=(5x)/3 ,\quad y=-(5x)/3

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asymptotes of (x^2)/9-(y^2)/(25)=1

asymptotes

\frac{x ^{2}}{9} - \frac{y ^{2}}{25} = 1

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

Solution steps

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

Calculate Hyperbola properties

\frac{x ^{2}}{9} - \frac{y ^{2}}{25} = 1 :

Right-left Hyperbola with

(h, k) = (0, 0), a = 3, b = 5

y = \frac{5}{3} (x - 0) + 0, y = - \frac{5}{3} (x - 0) + 0

Refine

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

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

\frac{y ^{2}}{4} - \frac{x ^{2}}{25} = 1

\frac{x ^{2}}{3} - \frac{y ^{2}}{3} = 1

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

- 16 x^{2} + 9 y^{2} + 96 x - 90 y - 63 = 0

What is the asymptotes of (x^2)/9-(y^2)/(25)=1 ?
The asymptotes of (x^2)/9-(y^2)/(25)=1 is y=(5x)/3 ,\quad y=-(5x)/3