What is the foci 2x^2+y^2+12x-6y+26=0 ?

The foci 2x^2+y^2+12x-6y+26=0 is (-3,3+sqrt(1/2)),(-3,3-sqrt(1/2))

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foci 2x^2+y^2+12x-6y+26=0

foci

2 x^{2} + y^{2} + 12 x - 6 y + 26 = 0

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

Solution steps

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

Calculate ellipse properties

2 x^{2} + y^{2} + 12 x - 6 y + 26 = 0 :

Ellipse with center

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

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

Compute

c :

c = 1^{2} - \frac{1}{2}^{2} : \frac{1}{2}

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

\frac{( x - h ) ^{2}}{a ^{2}} + \frac{( y - k ) ^{2}}{b ^{2}} = 1

\frac{( x - 3 ) ^{2}}{49} + \frac{( y + 5 ) ^{2}}{25} = 1

\frac{x ^{2}}{8} + \frac{y ^{2}}{4} = 1

9 x^{2} + 16 y^{2} = 576

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

What is the foci 2x^2+y^2+12x-6y+26=0 ?
The foci 2x^2+y^2+12x-6y+26=0 is (-3,3+sqrt(1/2)),(-3,3-sqrt(1/2))