What is the foci 3x^2+y^2+18x-2y-8=0 ?

The foci 3x^2+y^2+18x-2y-8=0 is (-3,1+2sqrt(6)),(-3,1-2sqrt(6))

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foci 3x^2+y^2+18x-2y-8=0

foci

3 x^{2} + y^{2} + 18 x - 2 y - 8 = 0

(- 3, 1 + 26), (- 3, 1 - 26)

Solution steps

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

Calculate ellipse properties

3 x^{2} + y^{2} + 18 x - 2 y - 8 = 0 :

Ellipse with center

(h, k) = (- 3, 1), b = 6, a = 23

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

Compute

c :

c = 6^{2} - (23)^{2} : 26

(- 3, 1 + 26), (- 3, 1 - 26)

\frac{( x - 8 ) ^{2}}{49} + \frac{( y + 1 ) ^{2}}{100} = 1

\frac{( x - 1 ) ^{2}}{36} + \frac{( y + 2 ) ^{2}}{25} = 1

36 x^{2} + 9 y^{2} + 36 y - 288 = 0

100 x^{2} + 36 y^{2} = 225

\frac{y ^{2}}{16} + \frac{x ^{2}}{9} = 1

What is the foci 3x^2+y^2+18x-2y-8=0 ?
The foci 3x^2+y^2+18x-2y-8=0 is (-3,1+2sqrt(6)),(-3,1-2sqrt(6))