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

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

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asymptotes of (x^2)/4-(y^2)/(25)=1

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

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

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}}{16} - \frac{x ^{2}}{4} = 1

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

\frac{( x - 2 ) ^{2}}{4} - \frac{( y + 3 ) ^{2}}{9} = 1

16 x^{2} - 9 y^{2} + 32 x + 72 y - 704 = 0

- 9 x^{2} + 16 y^{2} - 90 x + 128 y - 113 = 0

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