What is the foci 18x^2+8y^2+36x-32y-22=0 ?

The foci 18x^2+8y^2+36x-32y-22=0 is (-1,2+sqrt(5)),(-1,2-sqrt(5))

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foci 18x^2+8y^2+36x-32y-22=0

foci

18 x^{2} + 8 y^{2} + 36 x - 32 y - 22 = 0

(- 1, 2 + 5), (- 1, 2 - 5)

Solution steps

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

Calculate ellipse properties

18 x^{2} + 8 y^{2} + 36 x - 32 y - 22 = 0 :

Ellipse with center

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

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

Compute

c :

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

(- 1, 2 + 5), (- 1, 2 - 5)

\frac{x ^{2}}{32} + \frac{y ^{2}}{9} = 1

4 x^{2} + 25 y^{2} - 24 x + 250 y + 561 = 0

14 x^{2} - 70 = - 5 y^{2}

- \frac{( y - 1 ) ^{2}}{144} - \frac{( x + 2 ) ^{2}}{9} = 1

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

What is the foci 18x^2+8y^2+36x-32y-22=0 ?
The foci 18x^2+8y^2+36x-32y-22=0 is (-1,2+sqrt(5)),(-1,2-sqrt(5))