What is the foci 4x^2+9y^2+16x+18y-11=0 ?

The foci 4x^2+9y^2+16x+18y-11=0 is (-2+sqrt(5),-1),(-2-sqrt(5),-1)

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foci 4x^2+9y^2+16x+18y-11=0

foci

4 x^{2} + 9 y^{2} + 16 x + 18 y - 11 = 0

(- 2 + 5, - 1), (- 2 - 5, - 1)

Solution steps

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

Calculate ellipse properties

4 x^{2} + 9 y^{2} + 16 x + 18 y - 11 = 0 :

Ellipse with center

(h, k) = (- 2, - 1), a = 3, b = 2

(- 2 + c, - 1), (- 2 - c, - 1)

Compute

c :

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

(- 2 + 5, - 1), (- 2 - 5, - 1)

\frac{x ^{2}}{144} + \frac{y ^{2}}{225} = 1

4 x^{2} + 25 y^{2} + 40 x - 150 y + 225 = 0

\frac{x ^{2}}{\frac{81}{4}} + \frac{y ^{2}}{\frac{25}{16}} = 1

2 x^{2} + 3 y^{2} + 4 x - 1 = 0

x^{2} + \frac{( y - 6 ) ^{2}}{16} = 1

What is the foci 4x^2+9y^2+16x+18y-11=0 ?
The foci 4x^2+9y^2+16x+18y-11=0 is (-2+sqrt(5),-1),(-2-sqrt(5),-1)