What is the foci (x+4)^2+9(y-3)^2=81 ?

The foci (x+4)^2+9(y-3)^2=81 is (-4+6sqrt(2),3),(-4-6sqrt(2),3)

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foci (x+4)^2+9(y-3)^2=81

foci

(x + 4)^{2} + 9 (y - 3)^{2} = 81

(- 4 + 62, 3), (- 4 - 62, 3)

Solution steps

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

Calculate ellipse properties

(x + 4)^{2} + 9 (y - 3)^{2} = 81 :

Ellipse with center

(h, k) = (- 4, 3), a = 9, b = 3

(- 4 + c, 3), (- 4 - c, 3)

Compute

c :

c = 9^{2} - 3^{2} : 62

(- 4 + 62, 3), (- 4 - 62, 3)

\frac{( x + 2 ) ^{2}}{16} + \frac{( y - 2 ) ^{2}}{9} = 1

4 x^{2} + 25 y^{2} - 50 y - 75 = 0

\frac{( x - 11 ) ^{2}}{14} + \frac{( y - 13 ) ^{2}}{81} = 1

25 x^{2} + 4 y^{2} + 50 x - 16 y = 59

3 x^{2} + 7 y^{2} - 21 = 0

What is the foci (x+4)^2+9(y-3)^2=81 ?
The foci (x+4)^2+9(y-3)^2=81 is (-4+6sqrt(2),3),(-4-6sqrt(2),3)