What is the foci 9x^2+4y^2+18x-8y-131=0 ?

The foci 9x^2+4y^2+18x-8y-131=0 is (-1,1+2sqrt(5)),(-1,1-2sqrt(5))

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foci 9x^2+4y^2+18x-8y-131=0

foci

9 x^{2} + 4 y^{2} + 18 x - 8 y - 131 = 0

(- 1, 1 + 25), (- 1, 1 - 25)

Solution steps

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

Calculate ellipse properties

9 x^{2} + 4 y^{2} + 18 x - 8 y - 131 = 0 :

Ellipse with center

(h, k) = (- 1, 1), b = 6, a = 4

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

Compute

c :

c = 6^{2} - 4^{2} : 25

(- 1, 1 + 25), (- 1, 1 - 25)

\frac{( x - 2 ) ^{2}}{225} + \frac{( y - 8 ) ^{2}}{81} = 1

x^{2} + 2 y^{2} + 2 x - 20 y + 43 = 0

\frac{x ^{2}}{4} + \frac{y ^{2}}{3} = 1

2 x^{2} + 3 y^{2} + 10 x + 10 y - 10 = 0

\frac{( x - 4 ) ^{2}}{9} + \frac{( y + 6 ) ^{2}}{4} = 1

What is the foci 9x^2+4y^2+18x-8y-131=0 ?
The foci 9x^2+4y^2+18x-8y-131=0 is (-1,1+2sqrt(5)),(-1,1-2sqrt(5))