What is the foci 4x^2+9y^2+12x-108y+297=0 ?

The foci 4x^2+9y^2+12x-108y+297=0 is ((-3+2sqrt(5))/2 ,6),((-3-2sqrt(5))/2 ,6)

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foci 4x^2+9y^2+12x-108y+297=0

foci

(\frac{- 3 + 2 5}{2}, 6), (\frac{- 3 - 2 5}{2}, 6)

Solution steps

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

Calculate ellipse properties

4 x^{2} + 9 y^{2} + 12 x - 108 y + 297 = 0 :

Ellipse with center

(h, k) = (- \frac{3}{2}, 6), a = 3, b = 2

(- \frac{3}{2} + c, 6), (- \frac{3}{2} - c, 6)

Compute

c :

c = 3^{2} - 2^{2} : 5

(- \frac{3}{2} + 5, 6), (- \frac{3}{2} - 5, 6)

Refine

(\frac{- 3 + 2 5}{2}, 6), (\frac{- 3 - 2 5}{2}, 6)

What is the foci 4x^2+9y^2+12x-108y+297=0 ?
The foci 4x^2+9y^2+12x-108y+297=0 is ((-3+2sqrt(5))/2 ,6),((-3-2sqrt(5))/2 ,6)