What is the asymptotes of x^2-y^2-2x-2y-4=0 ?

The asymptotes of x^2-y^2-2x-2y-4=0 is y=x-2,\quad y=-(x-1)-1

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asymptotes of x^2-y^2-2x-2y-4=0

asymptotes

x^{2} - y^{2} - 2 x - 2 y - 4 = 0

y = x - 2, y = - (x - 1) - 1

Solution steps

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

Calculate Hyperbola properties

x^{2} - y^{2} - 2 x - 2 y - 4 = 0 :

Right-left Hyperbola with

(h, k) = (1, - 1), a = 2, b = 2

y = \frac{2}{2} (x - 1) + (- 1), y = - \frac{2}{2} (x - 1) + (- 1)

Refine

y = x - 2, y = - (x - 1) - 1

4 y^{2} - 2 x^{2} + 24 y - 8 x - 9 = 0

\frac{( x - 5 ) ^{2}}{1} - \frac{( y - 4 ) ^{2}}{1} = 1

(x - 2)^{2} - \frac{( y + 3 ) ^{2}}{9} = 1

16 x^{2} - 9 y^{2} - 32 x + 36 y + 124 = 0

- 3 x^{2} + 2 y^{2} + 6 x - 7 y = 7

What is the asymptotes of x^2-y^2-2x-2y-4=0 ?
The asymptotes of x^2-y^2-2x-2y-4=0 is y=x-2,\quad y=-(x-1)-1