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

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

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

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

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

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

Refine

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

\frac{( y - 2 ) ^{2}}{9} - \frac{( x + 3 ) ^{2}}{1} = 1

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

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}

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