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

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

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

foci

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

(- 1, 2 + 22), (- 1, 2 - 22)

Solution steps

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

Calculate ellipse properties

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

Ellipse with center

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

(- 1, 2 + c), (- 1, 2 - c)

Compute

c :

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

(- 1, 2 + 22), (- 1, 2 - 22)

\frac{x ^{2}}{32} + \frac{y ^{2}}{16} = 1

\frac{x ^{2}}{100} + \frac{( y - 6 ) ^{2}}{64} = 1

6 x^{2} + 9 y^{2} - 18 y - 45 = 0

\frac{( x - 1 ) ^{2}}{9} + \frac{( y + 2 ) ^{2}}{5} = 1

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

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