What is the foci 4x^2+9y^2+8x-36y+4=0 ?

The foci 4x^2+9y^2+8x-36y+4=0 is (-1+sqrt(5),2),(-1-sqrt(5),2)

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foci 4x^2+9y^2+8x-36y+4=0

foci

4 x^{2} + 9 y^{2} + 8 x - 36 y + 4 = 0

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

Solution steps

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

Calculate ellipse properties

4 x^{2} + 9 y^{2} + 8 x - 36 y + 4 = 0 :

Ellipse with center

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

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

Compute

c :

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

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

\frac{x ^{2}}{25} + \frac{y ^{2}}{36} = 1

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

9 x^{2} + 16 y^{2} - 54 x + 64 y + 1 = 0

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

9 x^{2} + 16 y^{2} + 126 x + 96 y + 441 = 0

What is the foci 4x^2+9y^2+8x-36y+4=0 ?
The foci 4x^2+9y^2+8x-36y+4=0 is (-1+sqrt(5),2),(-1-sqrt(5),2)