What is the foci 4x^2+9y^2+32x-18y+37=0 ?

The foci 4x^2+9y^2+32x-18y+37=0 is (-4+sqrt(5),1),(-4-sqrt(5),1)

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foci 4x^2+9y^2+32x-18y+37=0

foci

4 x^{2} + 9 y^{2} + 32 x - 18 y + 37 = 0

(- 4 + 5, 1), (- 4 - 5, 1)

Solution steps

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

Calculate ellipse properties

4 x^{2} + 9 y^{2} + 32 x - 18 y + 37 = 0 :

Ellipse with center

(h, k) = (- 4, 1), a = 3, b = 2

(- 4 + c, 1), (- 4 - c, 1)

Compute

c :

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

(- 4 + 5, 1), (- 4 - 5, 1)

16 x^{2} - 96 x + 4 y^{2} = - 80

3 x^{2} + y^{2} + 18 x - 2 y - 8 = 0

\frac{( x - 8 ) ^{2}}{49} + \frac{( y + 1 ) ^{2}}{100} = 1

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

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

What is the foci 4x^2+9y^2+32x-18y+37=0 ?
The foci 4x^2+9y^2+32x-18y+37=0 is (-4+sqrt(5),1),(-4-sqrt(5),1)