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

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

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

foci

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

(- 3 + 2, 0), (- 3 - 2, 0)

Solution steps

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

Calculate ellipse properties

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

Ellipse with center

(h, k) = (- 3, 0), a = 3, b = 1

(- 3 + c, 0), (- 3 - c, 0)

Compute

c :

c = 3^{2} - 1^{2} : 2

(- 3 + 2, 0), (- 3 - 2, 0)

16 x^{2} + 25 y^{2} - 48 x + 100 y - 264 = 0

9 x^{2} + 25 y^{2} + 54 x + 100 y - 44 = 0

15 x^{2} + 16 y^{2} = 240

\frac{( x - 3 ) ^{2}}{49} + \frac{( y - 5 ) ^{2}}{4} = 1

\frac{( x - 1 ) ^{2}}{45} + \frac{( y - 2 ) ^{2}}{20} = 1

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