What is the foci 9x^2+36x+y^2+2y+36=0 ?

The foci 9x^2+36x+y^2+2y+36=0 is (-2,(-3+2sqrt(2))/3),(-2,(-3-2sqrt(2))/3)

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foci 9x^2+36x+y^2+2y+36=0

foci

9 x^{2} + 36 x + y^{2} + 2 y + 36 = 0

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

Solution steps

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

Calculate ellipse properties

9 x^{2} + 36 x + y^{2} + 2 y + 36 = 0 :

Ellipse with center

(h, k) = (- 2, - 1), b = 1, a = \frac{1}{3}

(- 2, - 1 + c), (- 2, - 1 - c)

Compute

c :

c = 1^{2} - (\frac{1}{3})^{2} : \frac{2 2}{3}

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

Refine

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

\frac{( x - 4 ) ^{2}}{9} + (y + 3)^{2} = 1

2 x^{2} + 5 y^{2} = 10

x^{2} + 4 y^{2} - 2 x - 16 y + 13 = 0

4 x^{2} + 9 y^{2} = 25

4 y^{2} + 2 x^{2} - 4 y - 8 x - 15 = 0

What is the foci 9x^2+36x+y^2+2y+36=0 ?
The foci 9x^2+36x+y^2+2y+36=0 is (-2,(-3+2sqrt(2))/3),(-2,(-3-2sqrt(2))/3)