What is the asymptotes of x^2-y^2-4x-2y-13=0 ?

The asymptotes of x^2-y^2-4x-2y-13=0 is y=x-3,\quad y=-(x-2)-1

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asymptotes of x^2-y^2-4x-2y-13=0

asymptotes

x^{2} - y^{2} - 4 x - 2 y - 13 = 0

y = x - 3, y = - (x - 2) - 1

Solution steps

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

Calculate Hyperbola properties

x^{2} - y^{2} - 4 x - 2 y - 13 = 0 :

Right-left Hyperbola with

(h, k) = (2, - 1), a = 4, b = 4

y = \frac{4}{4} (x - 2) + (- 1), y = - \frac{4}{4} (x - 2) + (- 1)

Refine

y = x - 3, y = - (x - 2) - 1

- 4 x^{2} + y^{2} - 2 y = 3

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

- x^{2} + y^{2} = 1

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

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

What is the asymptotes of x^2-y^2-4x-2y-13=0 ?
The asymptotes of x^2-y^2-4x-2y-13=0 is y=x-3,\quad y=-(x-2)-1