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

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

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asymptotes of (x^2}{25}-\frac{y^2)/9 =1

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

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

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

Refine

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

x^{2} + y^{2} = 2

x^{2} + y^{2} - 6 x - 8 y = 0

y, y^{2} - x^{2} + 4 x + 8 y + 12 = 0

- 2 x^{2}

x^{2} + y = 4

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