What is the foci ((x+2)^2}{25}+\frac{(y-3)^2)/4 =1 ?

The foci ((x+2)^2}{25}+\frac{(y-3)^2)/4 =1 is (-2+sqrt(21),3),(-2-sqrt(21),3)

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foci ((x+2)^2}{25}+\frac{(y-3)^2)/4 =1

foci

\frac{( x + 2 ) ^{2}}{25} + \frac{( y - 3 ) ^{2}}{4} = 1

(- 2 + 21, 3), (- 2 - 21, 3)

Solution steps

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

Calculate ellipse properties

\frac{( x + 2 ) ^{2}}{25} + \frac{( y - 3 ) ^{2}}{4} = 1 :

Ellipse with center

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

(- 2 + c, 3), (- 2 - c, 3)

Compute

c :

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

(- 2 + 21, 3), (- 2 - 21, 3)

\frac{( x - 1 ) ^{2}}{8} + \frac{( y - 3 ) ^{2}}{4} = 1

\frac{x ^{2}}{4} + \frac{y ^{2}}{20} = 1

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

\frac{x ^{2}}{32} + \frac{y ^{2}}{18} = 1

x^{2} + \frac{y ^{2}}{100} = 1

What is the foci ((x+2)^2}{25}+\frac{(y-3)^2)/4 =1 ?
The foci ((x+2)^2}{25}+\frac{(y-3)^2)/4 =1 is (-2+sqrt(21),3),(-2-sqrt(21),3)