What is the asymptotes of x^2-3y^2-2x-6y+7=0 ?

The asymptotes of x^2-3y^2-2x-6y+7=0 is y=(x-1)/(sqrt(3))-1,\quad y=-(x-1)/(sqrt(3))-1

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asymptotes of x^2-3y^2-2x-6y+7=0

asymptotes

x^{2} - 3 y^{2} - 2 x - 6 y + 7 = 0

y = \frac{x - 1}{3} - 1, y = - \frac{x - 1}{3} - 1

Solution steps

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

Calculate Hyperbola properties

x^{2} - 3 y^{2} - 2 x - 6 y + 7 = 0 :

Up-down Hyperbola with

(h, k) = (1, - 1), a = 3, b = 3

y = \frac{3}{3} (x - 1) + (- 1), y = - \frac{3}{3} (x - 1) + (- 1)

Refine

y = \frac{x - 1}{3} - 1, y = - \frac{x - 1}{3} - 1

16 x^{2} - 9 y^{2} - 96 x + 288 = 0

10 x^{2} - 25 y^{2} = 100

(x - 4)^{2} - (y + 1)^{2} = 25

- 9 x^{2} + 8 y^{2} + 36 x + 48 y = 36

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

What is the asymptotes of x^2-3y^2-2x-6y+7=0 ?
The asymptotes of x^2-3y^2-2x-6y+7=0 is y=(x-1)/(sqrt(3))-1,\quad y=-(x-1)/(sqrt(3))-1