What is the foci 9x^2+4y^2-36x+40y+100=0 ?

The foci 9x^2+4y^2-36x+40y+100=0 is (2,-5+sqrt(5)),(2,-5-sqrt(5))

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foci 9x^2+4y^2-36x+40y+100=0

foci

9 x^{2} + 4 y^{2} - 36 x + 40 y + 100 = 0

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

Solution steps

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

Calculate ellipse properties

9 x^{2} + 4 y^{2} - 36 x + 40 y + 100 = 0 :

Ellipse with center

(h, k) = (2, - 5), b = 3, a = 2

(2, - 5 + c), (2, - 5 - c)

Compute

c :

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

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

x^{2} + y^{2} - 2 y = 0

\frac{x ^{2}}{12} + \frac{( y - 4 ) ^{2}}{16} = 1

\frac{( x + 2 ) ^{2}}{16} + \frac{( y + 2 ) ^{2}}{25} = 1

\frac{x ^{2}}{96} + \frac{y ^{2}}{100} = 1

9 x^{2} + 25 y^{2} - 100 y - 125 = 0

What is the foci 9x^2+4y^2-36x+40y+100=0 ?
The foci 9x^2+4y^2-36x+40y+100=0 is (2,-5+sqrt(5)),(2,-5-sqrt(5))