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

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

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

asymptotes

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

y = 5 x, y = - 5 x

Solution steps

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

Calculate Hyperbola properties

- 25 x^{2} + y^{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

5 x^{2} - 6 y^{2} - 20 x + 12 y - 16 = 0

\frac{y ^{2}}{1 2 ^{2}} - \frac{x ^{2}}{6 ^{2}} = 1

x^{2} - 4 (y - 3)^{2} = 4

16 y^{2} - 81 x^{2} - 256 y + 486 x = 1001

4 x^{2} - y^{2} + 40 x - 4 y + 80 = 0

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