What is the foci 9x^2+4y^2+36x-24y+36=0 ?

The foci 9x^2+4y^2+36x-24y+36=0 is (-2,3+sqrt(5)),(-2,3-sqrt(5))

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foci 9x^2+4y^2+36x-24y+36=0

foci

9 x^{2} + 4 y^{2} + 36 x - 24 y + 36 = 0

(- 2, 3 + 5), (- 2, 3 - 5)

Solution steps

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

Calculate ellipse properties

9 x^{2} + 4 y^{2} + 36 x - 24 y + 36 = 0 :

Ellipse with center

(h, k) = (- 2, 3), b = 3, a = 2

(- 2, 3 + c), (- 2, 3 - c)

Compute

c :

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

(- 2, 3 + 5), (- 2, 3 - 5)

y = - \frac{x ^{2}}{10} + \frac{9 x}{10} + \frac{11}{5}

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

y^{2} = 6 x

4 x^{2} + y^{2} + 8 x - 4 y + 4 = 0

y, y^{2} = x^{2}

What is the foci 9x^2+4y^2+36x-24y+36=0 ?
The foci 9x^2+4y^2+36x-24y+36=0 is (-2,3+sqrt(5)),(-2,3-sqrt(5))