What is the foci 9x^2+36y^2+36x+432y=-1008 ?

The foci 9x^2+36y^2+36x+432y=-1008 is (-2+3sqrt(3),-6),(-2-3sqrt(3),-6)

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foci 9x^2+36y^2+36x+432y=-1008

foci

9 x^{2} + 36 y^{2} + 36 x + 432 y = - 1008

(- 2 + 33, - 6), (- 2 - 33, - 6)

Solution steps

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

Calculate ellipse properties

9 x^{2} + 36 y^{2} + 36 x + 432 y = - 1008 :

Ellipse with center

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

(- 2 + c, - 6), (- 2 - c, - 6)

Compute

c :

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

(- 2 + 33, - 6), (- 2 - 33, - 6)

4 x^{2} + 9 y^{2} - 32 x - 36 y + 64 = 0

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

9 x^{2} - 54 x + y^{2} + 2 y + 46 = 0

\frac{x ^{2}}{49} + \frac{y ^{2}}{4} = 1

\frac{x ^{2}}{3. 2 ^{2}} + \frac{y ^{2}}{2.4 8 ^{2}} = 1

What is the foci 9x^2+36y^2+36x+432y=-1008 ?
The foci 9x^2+36y^2+36x+432y=-1008 is (-2+3sqrt(3),-6),(-2-3sqrt(3),-6)