What is the foci 4x^2+9y^2+24x-36y+36=0 ?

The foci 4x^2+9y^2+24x-36y+36=0 is (-3+sqrt(5),2),(-3-sqrt(5),2)

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foci 4x^2+9y^2+24x-36y+36=0

foci

4 x^{2} + 9 y^{2} + 24 x - 36 y + 36 = 0

(- 3 + 5, 2), (- 3 - 5, 2)

Solution steps

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

Calculate ellipse properties

4 x^{2} + 9 y^{2} + 24 x - 36 y + 36 = 0 :

Ellipse with center

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

(- 3 + c, 2), (- 3 - c, 2)

Compute

c :

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

(- 3 + 5, 2), (- 3 - 5, 2)

4 x^{2} + 16 y^{2} - 16 x - 48 = 0

\frac{( x + 3 ) ^{2}}{9} + \frac{( y - 1 ) ^{2}}{25} = 1

4 x^{2} + 9 y^{2} - 48 x + 72 y = - 144

36 x^{2} + 16 y^{2} - 180 x + 96 y - 207 = 0

x^{2} + 2 y^{2} + 2 x - 4 y - 1 = 0

What is the foci 4x^2+9y^2+24x-36y+36=0 ?
The foci 4x^2+9y^2+24x-36y+36=0 is (-3+sqrt(5),2),(-3-sqrt(5),2)