What is the asymptotes of (x^2}{25}-\frac{y^2)/4 =1 ?

The asymptotes of (x^2}{25}-\frac{y^2)/4 =1 is y=(2x)/5 ,\quad y=-(2x)/5

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asymptotes of (x^2}{25}-\frac{y^2)/4 =1

asymptotes

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

y = \frac{2 x}{5}, y = - \frac{2 x}{5}

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

(h, k) = (0, 0), a = 5, b = 2

y = \frac{2}{5} (x - 0) + 0, y = - \frac{2}{5} (x - 0) + 0

Refine

y = \frac{2 x}{5}, y = - \frac{2 x}{5}

25 y^{2} - 36 (x - 8)^{2} = 900

\frac{x ^{2}}{25} - \frac{y ^{2}}{49} = 1

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

16 x^{2} - 25 y^{2} = 100

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

What is the asymptotes of (x^2}{25}-\frac{y^2)/4 =1 ?
The asymptotes of (x^2}{25}-\frac{y^2)/4 =1 is y=(2x)/5 ,\quad y=-(2x)/5