What is the foci x^2+9y^2+6x-90y+225=0 ?

The foci x^2+9y^2+6x-90y+225=0 is (-3+2sqrt(2),5),(-3-2sqrt(2),5)

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foci x^2+9y^2+6x-90y+225=0

foci

x^{2} + 9 y^{2} + 6 x - 90 y + 225 = 0

(- 3 + 22, 5), (- 3 - 22, 5)

Solution steps

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

Calculate ellipse properties

x^{2} + 9 y^{2} + 6 x - 90 y + 225 = 0 :

Ellipse with center

(h, k) = (- 3, 5), a = 3, b = 1

(- 3 + c, 5), (- 3 - c, 5)

Compute

c :

c = 3^{2} - 1^{2} : 22

(- 3 + 22, 5), (- 3 - 22, 5)

x^{2} + 3 y^{2} - 4 x + 12 y + 13 = 0

49 x^{2} + 25 y^{2} = 1225

\frac{x ^{2}}{64} + \frac{y ^{2}}{49} = 1

3 x^{2} + 12 y^{2} - 6 x - 48 y + 33 = 0

16 x^{2} - 64 x + 9 y^{2} = 80

What is the foci x^2+9y^2+6x-90y+225=0 ?
The foci x^2+9y^2+6x-90y+225=0 is (-3+2sqrt(2),5),(-3-2sqrt(2),5)