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

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

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

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

Right-left 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)

- 16 x^{2} + 9 y^{2} + 96 x - 90 y - 63 = 0

- 4 x^{2} + y^{2} = 16

\frac{x ^{2}}{64} - \frac{y ^{2}}{144} = 1

\frac{x ^{2}}{4} - \frac{y ^{2}}{25} = 1

\frac{y ^{2}}{16} - \frac{x ^{2}}{4} = 1

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