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

The asymptotes of y^2-25x^2=25 is y=5x,\quad y=-5x

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

asymptotes

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

y = 5 x, y = - 5 x

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

(h, k) = (0, 0), a = 5, b = 1

y = \frac{5}{1} (x - 0) + 0, y = - \frac{5}{1} (x - 0) + 0

Refine

y = 5 x, y = - 5 x

\frac{( x - 2 ) ^{2}}{4} - \frac{( y + 3 ) ^{2}}{5} = 1

\frac{( x + 2 ) ^{2}}{36} - y^{2} = 1

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

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

8 x^{2} - 2 y^{2} = 16

What is the asymptotes of y^2-25x^2=25 ?
The asymptotes of y^2-25x^2=25 is y=5x,\quad y=-5x