What is the foci 4x^2+9y^2+16x-90y+205=0 ?

The foci 4x^2+9y^2+16x-90y+205=0 is (-2+sqrt(5),5),(-2-sqrt(5),5)

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foci 4x^2+9y^2+16x-90y+205=0

foci

4 x^{2} + 9 y^{2} + 16 x - 90 y + 205 = 0

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

Solution steps

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

Calculate ellipse properties

4 x^{2} + 9 y^{2} + 16 x - 90 y + 205 = 0 :

Ellipse with center

(h, k) = (- 2, 5), a = 3, b = 2

(- 2 + c, 5), (- 2 - c, 5)

Compute

c :

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

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

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

\frac{( x - 1 ) ^{2}}{36} + \frac{( y - 2 ) ^{2}}{115} = 3

\frac{( x - 2 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{5} = 1

\frac{( x - 3 ) ^{2}}{100} + \frac{( y - 1 ) ^{2}}{64} = 1

25 x^{2} + y^{2} - 4 y - 21 = 0

What is the foci 4x^2+9y^2+16x-90y+205=0 ?
The foci 4x^2+9y^2+16x-90y+205=0 is (-2+sqrt(5),5),(-2-sqrt(5),5)