What is the asymptotes of 16x^2-25y^2=100 ?

The asymptotes of 16x^2-25y^2=100 is y=(4x)/5 ,\quad y=-(4x)/5

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asymptotes of 16x^2-25y^2=100

asymptotes

16 x^{2} - 25 y^{2} = 100

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

Solution steps

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

Calculate Hyperbola properties

16 x^{2} - 25 y^{2} = 100 :

Right-left Hyperbola with

(h, k) = (0, 0), a = \frac{5}{2}, b = 2

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

Refine

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

- x^{2} + 4 y^{2} = 16

\frac{( x + 9 ) ^{2}}{9} - \frac{( y - 8 ) ^{2}}{4} = 1

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

9 x^{2} - 16 y^{2} - 18 x + 64 y - 199 = 0

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

What is the asymptotes of 16x^2-25y^2=100 ?
The asymptotes of 16x^2-25y^2=100 is y=(4x)/5 ,\quad y=-(4x)/5