What is the foci 25x^2-200x+y^2+4y+379=0 ?

The foci 25x^2-200x+y^2+4y+379=0 is (4,-2+2sqrt(6)),(4,-2-2sqrt(6))

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foci 25x^2-200x+y^2+4y+379=0

foci

25 x^{2} - 200 x + y^{2} + 4 y + 379 = 0

(4, - 2 + 26), (4, - 2 - 26)

Solution steps

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

Calculate ellipse properties

25 x^{2} - 200 x + y^{2} + 4 y + 379 = 0 :

Ellipse with center

(h, k) = (4, - 2), b = 5, a = 1

(4, - 2 + c), (4, - 2 - c)

Compute

c :

c = 5^{2} - 1^{2} : 26

(4, - 2 + 26), (4, - 2 - 26)

64 x^{2} + 100 y^{2} + 768 x - 600 y - 3196 = 0

\frac{x ^{2}}{16} + \frac{y ^{2}}{12} = 1

\frac{x ^{2}}{16} + (y - 4)^{2} = 1

3 x^{2} + y^{2} - 24 x + 39 = 0

9 x^{2} - 18 x + 4 y^{2} = 27

What is the foci 25x^2-200x+y^2+4y+379=0 ?
The foci 25x^2-200x+y^2+4y+379=0 is (4,-2+2sqrt(6)),(4,-2-2sqrt(6))