What is the foci ((x-4)^2)/9+((y-2)^2)/4 =1 ?

The foci ((x-4)^2)/9+((y-2)^2)/4 =1 is (4+sqrt(5),2),(4-sqrt(5),2)

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foci ((x-4)^2)/9+((y-2)^2)/4 =1

foci

\frac{( x - 4 ) ^{2}}{9} + \frac{( y - 2 ) ^{2}}{4} = 1

(4 + 5, 2), (4 - 5, 2)

Solution steps

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

Calculate ellipse properties

\frac{( x - 4 ) ^{2}}{9} + \frac{( y - 2 ) ^{2}}{4} = 1 :

Ellipse with center

(h, k) = (4, 2), a = 3, b = 2

(4 + c, 2), (4 - c, 2)

Compute

c :

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

(4 + 5, 2), (4 - 5, 2)

\frac{x ^{2}}{63500} + \frac{y ^{2}}{50900} = 1

\frac{( x - 6 ) ^{2}}{16} + \frac{( y + 3 ) ^{2}}{25} = 1

4 x^{2} + 25 y^{2} + 24 x + 250 y = - 561

4 x^{2} + 36 y^{2} + 24 x + 432 y = - 1188

\frac{( x - 2 ) ^{2}}{16} + \frac{( y + 3 ) ^{2}}{9} = 1

What is the foci ((x-4)^2)/9+((y-2)^2)/4 =1 ?
The foci ((x-4)^2)/9+((y-2)^2)/4 =1 is (4+sqrt(5),2),(4-sqrt(5),2)