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

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

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

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

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

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

Refine

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

2 x^{2} - 2 y^{2} - 20 x + 16 y + 16 = 0

25 y^{2} - 16 x^{2} - 400 = 0

9 (y - 2)^{2} - 4 x^{2} = 36

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

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

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