What is the foci x^2-3y^2+2x+6y-1=0 ?

The foci x^2-3y^2+2x+6y-1=0 is (-1,(sqrt(3)+2)/(sqrt(3))),(-1,(sqrt(3)-2)/(sqrt(3)))

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foci x^2-3y^2+2x+6y-1=0

foci

x^{2} - 3 y^{2} + 2 x + 6 y - 1 = 0

(- 1, \frac{3 + 2}{3}), (- 1, \frac{3 - 2}{3})

Solution steps

(h, k + c), (h, k - c)

Calculate Hyperbola properties

x^{2} - 3 y^{2} + 2 x + 6 y - 1 = 0 :

Up-down Hyperbola with

(h, k) = (- 1, 1), a = \frac{1}{3}, b = 1

(- 1, 1 + c), (- 1, 1 - c)

Compute

c :

c = \frac{1}{3}^{2} + 1^{2} : \frac{2}{3}

(- 1, 1 + \frac{2}{3}), (- 1, 1 - \frac{2}{3})

Refine

(- 1, \frac{3 + 2}{3}), (- 1, \frac{3 - 2}{3})

- 4 x^{2} + 25 y^{2} - 16 x - 116 = 0

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

- \frac{( x + 1 ) ^{2}}{25} + \frac{( y + 5 ) ^{2}}{16} = 1

\frac{( x ^{2} )}{4} - 0.12 y^{2} = 1

9 y^{2} - 16 x^{2} = 81

What is the foci x^2-3y^2+2x+6y-1=0 ?
The foci x^2-3y^2+2x+6y-1=0 is (-1,(sqrt(3)+2)/(sqrt(3))),(-1,(sqrt(3)-2)/(sqrt(3)))