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

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

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

asymptotes

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

y = x - 1, y = - (x - 1)

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

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

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

Refine

y = x - 1, y = - (x - 1)

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

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

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

(x - 4)^{2} - (y - 5)^{2} = 15

\frac{x ^{2}}{81} - \frac{y ^{2}}{4} = 1

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