What is the asymptotes of (x^2)/(25)-(y^2)/(64)=1 ?

The asymptotes of (x^2)/(25)-(y^2)/(64)=1 is y=(8x)/5 ,\quad y=-(8x)/5

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asymptotes of (x^2)/(25)-(y^2)/(64)=1

asymptotes

\frac{x ^{2}}{25} - \frac{y ^{2}}{64} = 1

y = \frac{8 x}{5}, y = - \frac{8 x}{5}

Solution steps

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

Calculate Hyperbola properties

\frac{x ^{2}}{25} - \frac{y ^{2}}{64} = 1 :

Right-left Hyperbola with

(h, k) = (0, 0), a = 5, b = 8

y = \frac{8}{5} (x - 0) + 0, y = - \frac{8}{5} (x - 0) + 0

Refine

y = \frac{8 x}{5}, y = - \frac{8 x}{5}

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

y^{2} - 4 x^{2} + 4 x - 2 y - 4 = 0

16 y^{2} - x^{2} + 2 x + 64 y - 1 = 0

5 x^{2} - 5 y^{2} + 20 x - 60 y = 185

9 y^{2} - 4 x^{2} - 36 y - 8 x = 4

What is the asymptotes of (x^2)/(25)-(y^2)/(64)=1 ?
The asymptotes of (x^2)/(25)-(y^2)/(64)=1 is y=(8x)/5 ,\quad y=-(8x)/5