What is the asymptotes of x^2-y^2=100 ?

The asymptotes of x^2-y^2=100 is y=x,\quad y=-x

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asymptotes of x^2-y^2=100

asymptotes

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

y = x, y = - x

Solution steps

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

Calculate Hyperbola properties

x^{2} - y^{2} = 100 :

Right-left Hyperbola with

(h, k) = (0, 0), a = 10, b = 10

y = \frac{10}{10} (x - 0) + 0, y = - \frac{10}{10} (x - 0) + 0

Refine

y = x, y = - x

5 y^{2} - 16 x^{2} + 400 = 0

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

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

What is the asymptotes of x^2-y^2=100 ?
The asymptotes of x^2-y^2=100 is y=x,\quad y=-x