What is the asymptotes of 4x^2-25y^2+100y=200 ?

The asymptotes of 4x^2-25y^2+100y=200 is y=(2x)/5+2,\quad y=-(2x)/5+2

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asymptotes of 4x^2-25y^2+100y=200

asymptotes

4 x^{2} - 25 y^{2} + 100 y = 200

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

Solution steps

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

Calculate Hyperbola properties

4 x^{2} - 25 y^{2} + 100 y = 200 :

Right-left Hyperbola with

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

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

Refine

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

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

9 y^{2} - 49 x^{2} = 441

4 x^{2} - 9 y^{2} - 16 x + 18 y - 7 = 0

64 x^{2} - 100 y^{2} = 6400

\frac{x ^{2}}{3} - \frac{y ^{2}}{1.5} = 1

What is the asymptotes of 4x^2-25y^2+100y=200 ?
The asymptotes of 4x^2-25y^2+100y=200 is y=(2x)/5+2,\quad y=-(2x)/5+2