What is the foci 3x^2+2y^2+6x-4y+5=18 ?

The foci 3x^2+2y^2+6x-4y+5=18 is (-1,1+sqrt(3)),(-1,1-sqrt(3))

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foci 3x^2+2y^2+6x-4y+5=18

foci

3 x^{2} + 2 y^{2} + 6 x - 4 y + 5 = 18

(- 1, 1 + 3), (- 1, 1 - 3)

Solution steps

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

Calculate ellipse properties

3 x^{2} + 2 y^{2} + 6 x - 4 y + 5 = 18 :

Ellipse with center

(h, k) = (- 1, 1), b = 3, a = 6

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

Compute

c :

c = 3^{2} - 6^{2} : 3

(- 1, 1 + 3), (- 1, 1 - 3)

\frac{x ^{2}}{49} + \frac{y ^{2}}{25} = 1

\frac{( x + 2 ) ^{2}}{25} + \frac{( y - 1 ) ^{2}}{169} = 1

\frac{( x - 3 ) ^{2}}{25} + \frac{y ^{2}}{9} = 1

x^{2} + 4 y^{2} = 16

\frac{( x - 2 ) ^{2}}{36} + \frac{( y + 5 ) ^{2}}{9} = 1

What is the foci 3x^2+2y^2+6x-4y+5=18 ?
The foci 3x^2+2y^2+6x-4y+5=18 is (-1,1+sqrt(3)),(-1,1-sqrt(3))