What is the asymptotes of y^2=x^2-4x ?

The asymptotes of y^2=x^2-4x is y=x-2,\quad y=-(x-2)

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asymptotes of y^2=x^2-4x

asymptotes

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

y = x - 2, y = - (x - 2)

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

(h, k) = (2, 0), a = 2, b = 2

y = \frac{2}{2} (x - 2) + 0, y = - \frac{2}{2} (x - 2) + 0

Refine

y = x - 2, y = - (x - 2)

9 x^{2} - 16 y^{2} - 54 x + 64 y - 127 = 0

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

- 9 x^{2} + 4 y^{2} - 36 x - 16 y - 164 = 0

\frac{y ^{2}}{16} - \frac{x ^{2}}{36} = 1

x^{2} - y^{2} - 4 x + 8 y - 21 = 0

What is the asymptotes of y^2=x^2-4x ?
The asymptotes of y^2=x^2-4x is y=x-2,\quad y=-(x-2)