What is the foci ((x-1)^2)/(36)+((y-2)^2)/(115)=3 ?

The foci ((x-1)^2)/(36)+((y-2)^2)/(115)=3 is (1,2+sqrt(237)),(1,2-sqrt(237))

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foci ((x-1)^2)/(36)+((y-2)^2)/(115)=3

foci

\frac{( x - 1 ) ^{2}}{36} + \frac{( y - 2 ) ^{2}}{115} = 3

(1, 2 + 237), (1, 2 - 237)

Solution steps

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

Calculate ellipse properties

\frac{( x - 1 ) ^{2}}{36} + \frac{( y - 2 ) ^{2}}{115} = 3 :

Ellipse with center

(h, k) = (1, 2), b = 345, a = 63

(1, 2 + c), (1, 2 - c)

Compute

c :

c = 345^{2} - (63)^{2} : 237

(1, 2 + 237), (1, 2 - 237)

\frac{( x - 2 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{5} = 1

\frac{( x - 3 ) ^{2}}{100} + \frac{( y - 1 ) ^{2}}{64} = 1

25 x^{2} + y^{2} - 4 y - 21 = 0

16 x^{2} + 25 y^{2} - 64 x + 150 y = - 279

\frac{( x - 12 ) ^{2}}{100} + \frac{( y + 7 ) ^{2}}{36} = 1

What is the foci ((x-1)^2)/(36)+((y-2)^2)/(115)=3 ?
The foci ((x-1)^2)/(36)+((y-2)^2)/(115)=3 is (1,2+sqrt(237)),(1,2-sqrt(237))