What is the foci 4x^2+8x+2y^2+16y=-28 ?

The foci 4x^2+8x+2y^2+16y=-28 is (-1,-4+sqrt(2)),(-1,-4-sqrt(2))

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foci 4x^2+8x+2y^2+16y=-28

foci

4 x^{2} + 8 x + 2 y^{2} + 16 y = - 28

(- 1, - 4 + 2), (- 1, - 4 - 2)

Solution steps

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

Calculate ellipse properties

4 x^{2} + 8 x + 2 y^{2} + 16 y = - 28 :

Ellipse with center

(h, k) = (- 1, - 4), b = 2, a = 2

(- 1, - 4 + c), (- 1, - 4 - c)

Compute

c :

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

(- 1, - 4 + 2), (- 1, - 4 - 2)

x^{2} - 4 x + 100 y^{2} + 200 y + 4 = 0

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

\frac{( x - 9 ) ^{2}}{4} + \frac{( y + 10 ) ^{2}}{81} = 1

18 x^{2} + 8 y^{2} + 36 x - 32 y - 22 = 0

\frac{x ^{2}}{32} + \frac{y ^{2}}{9} = 1

What is the foci 4x^2+8x+2y^2+16y=-28 ?
The foci 4x^2+8x+2y^2+16y=-28 is (-1,-4+sqrt(2)),(-1,-4-sqrt(2))