What is the foci 9x^2+y^2+36x-2y+1=0 ?

The foci 9x^2+y^2+36x-2y+1=0 is (-2,1+4sqrt(2)),(-2,1-4sqrt(2))

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foci 9x^2+y^2+36x-2y+1=0

foci

9 x^{2} + y^{2} + 36 x - 2 y + 1 = 0

(- 2, 1 + 42), (- 2, 1 - 42)

Solution steps

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

Calculate ellipse properties

9 x^{2} + y^{2} + 36 x - 2 y + 1 = 0 :

Ellipse with center

(h, k) = (- 2, 1), b = 6, a = 2

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

Compute

c :

c = 6^{2} - 2^{2} : 42

(- 2, 1 + 42), (- 2, 1 - 42)

\frac{( x ) ^{2}}{46} + \frac{( y + 8 ) ^{2}}{26} = 1

\frac{( x - 4 ) ^{2}}{4} + \frac{( y - 5 ) ^{2}}{25} = 1

81 x^{2} + 36 y^{2} = 2916

5 x^{2} + 7 y^{2} = 70

x^{2} + 9 y^{2} + 4 x = 5

What is the foci 9x^2+y^2+36x-2y+1=0 ?
The foci 9x^2+y^2+36x-2y+1=0 is (-2,1+4sqrt(2)),(-2,1-4sqrt(2))