What is the foci ((x+6)^2)/4+((y+6)^2)/(25)=1 ?

The foci ((x+6)^2)/4+((y+6)^2)/(25)=1 is (-6,-6+sqrt(21)),(-6,-6-sqrt(21))

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foci ((x+6)^2)/4+((y+6)^2)/(25)=1

foci

\frac{( x + 6 ) ^{2}}{4} + \frac{( y + 6 ) ^{2}}{25} = 1

(- 6, - 6 + 21), (- 6, - 6 - 21)

Solution steps

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

Calculate ellipse properties

\frac{( x + 6 ) ^{2}}{4} + \frac{( y + 6 ) ^{2}}{25} = 1 :

Ellipse with center

(h, k) = (- 6, - 6), b = 5, a = 2

(- 6, - 6 + c), (- 6, - 6 - c)

Compute

c :

c = 5^{2} - 2^{2} : 21

(- 6, - 6 + 21), (- 6, - 6 - 21)

\frac{( x + 2 ) ^{2}}{25} + \frac{( y - 5 ) ^{2}}{9} = 1

\frac{( x + 4 ) ^{2}}{24} + \frac{( y + 2 ) ^{2}}{49} = 1

3 x^{2} + 4 y^{2} = 48

9 (x + 2)^{2} + 4 (y - 3)^{2} = 36

\frac{( x + 1 ) ^{2}}{25} + \frac{( y - 4 ) ^{2}}{169} = 1

What is the foci ((x+6)^2)/4+((y+6)^2)/(25)=1 ?
The foci ((x+6)^2)/4+((y+6)^2)/(25)=1 is (-6,-6+sqrt(21)),(-6,-6-sqrt(21))