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

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

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

foci

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

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

Solution steps

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

Calculate ellipse properties

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

Ellipse with center

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

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

Compute

c :

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

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

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

2 x^{2} + y^{2} = 50

\frac{( x - 5 ) ^{2}}{8 ^{2}} + \frac{( y + 2 ) ^{2}}{1 0 ^{2}} = 1

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

9 x^{2} - 54 x + 4 y^{2} = - 45

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