What is the foci 36x^2+5y^2-90y-495=0 ?

The foci 36x^2+5y^2-90y-495=0 is (0,9+sqrt(155)),(0,9-sqrt(155))

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foci 36x^2+5y^2-90y-495=0

foci

36 x^{2} + 5 y^{2} - 90 y - 495 = 0

(0, 9 + 155), (0, 9 - 155)

Solution steps

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

Calculate ellipse properties

36 x^{2} + 5 y^{2} - 90 y - 495 = 0 :

Ellipse with center

(h, k) = (0, 9), b = 65, a = 5

(0, 9 + c), (0, 9 - c)

Compute

c :

c = (65)^{2} - 5^{2} : 155

(0, 9 + 155), (0, 9 - 155)

16 x^{2} - 32 x + 9 y^{2} = 128

(\frac{x ^{2}}{15}) + (\frac{y ^{2}}{16}) = 1

9 x^{2} - 18 x + 25 y^{2} - 250 y + 409 = 0

25 x^{2} + 9 y^{2} + 50 x - 108 y + 124 = 0

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

What is the foci 36x^2+5y^2-90y-495=0 ?
The foci 36x^2+5y^2-90y-495=0 is (0,9+sqrt(155)),(0,9-sqrt(155))