What is the asymptotes of y^2-x^2= 9/25 ?

The asymptotes of y^2-x^2= 9/25 is y=x,\quad y=-x

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asymptotes of y^2-x^2= 9/25

asymptotes

y^{2} - x^{2} = \frac{9}{25}

y = x, y = - x

Solution steps

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

Calculate Hyperbola properties

y^{2} - x^{2} = \frac{9}{25} :

Up-down Hyperbola with

(h, k) = (0, 0), a = \frac{3}{5}, b = \frac{3}{5}

y = \frac{\frac{3}{5}}{\frac{3}{5}} (x - 0) + 0, y = - \frac{\frac{3}{5}}{\frac{3}{5}} (x - 0) + 0

Refine

y = x, y = - x

25 y^{2} - 64 x^{2} = 1600

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

9 x^{2} - y^{2} + 36 x - 12 y = 36

4 x^{2} - 24 x - 25 y^{2} + 250 y - 489 = 0

25 y^{2} - 81 x^{2} = 2025

What is the asymptotes of y^2-x^2= 9/25 ?
The asymptotes of y^2-x^2= 9/25 is y=x,\quad y=-x