What is the foci 25x^2+y^2-100x+8y+91=0 ?

The foci 25x^2+y^2-100x+8y+91=0 is (2,-4+2sqrt(6)),(2,-4-2sqrt(6))

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foci 25x^2+y^2-100x+8y+91=0

foci

25 x^{2} + y^{2} - 100 x + 8 y + 91 = 0

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

Solution steps

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

Calculate ellipse properties

25 x^{2} + y^{2} - 100 x + 8 y + 91 = 0 :

Ellipse with center

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

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

Compute

c :

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

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

9 x^{2} + 36 y^{2} = 324

\frac{( x - 12 ) ^{2}}{289} + \frac{( y - 3 ) ^{2}}{64} = 1

9 X^{2} + 4 Y^{2} = 36

\frac{x ^{2}}{9} + \frac{y ^{2}}{36} = 1

4 (x - 1)^{2} + 9 (y - 1)^{2} = 36

What is the foci 25x^2+y^2-100x+8y+91=0 ?
The foci 25x^2+y^2-100x+8y+91=0 is (2,-4+2sqrt(6)),(2,-4-2sqrt(6))