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

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

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

asymptotes

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

y = 5 x, y = - 5 x

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

(h, k) = (0, 0), a = 1, b = \frac{1}{5}

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

Refine

y = 5 x, y = - 5 x

4 x^{2} - 9 y^{2} - 16 x + 54 y - 101 = 0

\frac{( x - 1 ) ^{2}}{9} - \frac{( y + 3 ) ^{2}}{4} = 1

- 4 x^{2} + y^{2} = 36

\frac{y ^{2}}{36} - \frac{x ^{2}}{9} = 1

\frac{9 x ^{2}}{64} - \frac{y ^{2}}{16} = 1

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