What is the foci 36x^2+9y^2+36y-288=0 ?

The foci 36x^2+9y^2+36y-288=0 is (0,-2+3sqrt(3)),(0,-2-3sqrt(3))

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foci 36x^2+9y^2+36y-288=0

foci

36 x^{2} + 9 y^{2} + 36 y - 288 = 0

(0, - 2 + 33), (0, - 2 - 33)

Solution steps

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

Calculate ellipse properties

36 x^{2} + 9 y^{2} + 36 y - 288 = 0 :

Ellipse with center

(h, k) = (0, - 2), b = 6, a = 3

(0, - 2 + c), (0, - 2 - c)

Compute

c :

c = 6^{2} - 3^{2} : 33

(0, - 2 + 33), (0, - 2 - 33)

100 x^{2} + 36 y^{2} = 225

\frac{y ^{2}}{16} + \frac{x ^{2}}{9} = 1

x^{2} + 3 y^{2} - 6 x + 6 y = 0

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

\frac{( x - 3 ) ^{2}}{16} + \frac{y ^{2}}{9} = 1

What is the foci 36x^2+9y^2+36y-288=0 ?
The foci 36x^2+9y^2+36y-288=0 is (0,-2+3sqrt(3)),(0,-2-3sqrt(3))