What is the asymptotes of (x^2)/(16)-(y^2)/(25)=1 ?

The asymptotes of (x^2)/(16)-(y^2)/(25)=1 is y=(5x)/4 ,\quad y=-(5x)/4

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asymptotes of (x^2)/(16)-(y^2)/(25)=1

asymptotes

\frac{x ^{2}}{16} - \frac{y ^{2}}{25} = 1

y = \frac{5 x}{4}, y = - \frac{5 x}{4}

Solution steps

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

Calculate Hyperbola properties

\frac{x ^{2}}{16} - \frac{y ^{2}}{25} = 1 :

Right-left Hyperbola with

(h, k) = (0, 0), a = 4, b = 5

y = \frac{5}{4} (x - 0) + 0, y = - \frac{5}{4} (x - 0) + 0

Refine

y = \frac{5 x}{4}, y = - \frac{5 x}{4}

9 x^{2} - 18 x - 16 y^{2} - 64 y = 199

\frac{x ^{2}}{4} - \frac{y ^{2}}{5} = 1

x^{2} - y^{2} + 4 x - 6 y = 6

9 x^{2} - 4 y^{2} + 36 x - 8 y - 40 = 0

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

What is the asymptotes of (x^2)/(16)-(y^2)/(25)=1 ?
The asymptotes of (x^2)/(16)-(y^2)/(25)=1 is y=(5x)/4 ,\quad y=-(5x)/4