What is the foci 9x^2+18x+4y^2-24y+9=0 ?

The foci 9x^2+18x+4y^2-24y+9=0 is (-1,3+sqrt(5)),(-1,3-sqrt(5))

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foci 9x^2+18x+4y^2-24y+9=0

foci

9 x^{2} + 18 x + 4 y^{2} - 24 y + 9 = 0

(- 1, 3 + 5), (- 1, 3 - 5)

Solution steps

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

Calculate ellipse properties

9 x^{2} + 18 x + 4 y^{2} - 24 y + 9 = 0 :

Ellipse with center

(h, k) = (- 1, 3), b = 3, a = 2

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

Compute

c :

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

(- 1, 3 + 5), (- 1, 3 - 5)

x^{2} + 4 y^{2} - 6 x + 20 y - 2 = 0

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

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

25 x^{2} + 144 y^{2} = 900

3 x^{2} + 6 y^{2} = 18

What is the foci 9x^2+18x+4y^2-24y+9=0 ?
The foci 9x^2+18x+4y^2-24y+9=0 is (-1,3+sqrt(5)),(-1,3-sqrt(5))