What is the foci 25(x+2)^2+4(y-3)^2=100 ?

The foci 25(x+2)^2+4(y-3)^2=100 is (-2,3+sqrt(21)),(-2,3-sqrt(21))

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foci 25(x+2)^2+4(y-3)^2=100

foci

25 (x + 2)^{2} + 4 (y - 3)^{2} = 100

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

Solution steps

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

Calculate ellipse properties

25 (x + 2)^{2} + 4 (y - 3)^{2} = 100 :

Ellipse with center

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

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

Compute

c :

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

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

\frac{x ^{2}}{4 ^{2}} + \frac{y ^{2}}{3 ^{2}} = 1

16 x^{2} + 25 y^{2} - 224 x + 250 y = 191

\frac{( x - 1 ) ^{2}}{40} + \frac{( y + 4 ) ^{2}}{36} = 1

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

x^{2} + 4 y^{2} - 6 x + 8 y - 3 = 0

What is the foci 25(x+2)^2+4(y-3)^2=100 ?
The foci 25(x+2)^2+4(y-3)^2=100 is (-2,3+sqrt(21)),(-2,3-sqrt(21))