What is the foci ((x-11)^2)/(63)+((y-13)^2)/(81)=1 ?

The foci ((x-11)^2)/(63)+((y-13)^2)/(81)=1 is (11,13+3sqrt(2)),(11,13-3sqrt(2))

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foci ((x-11)^2)/(63)+((y-13)^2)/(81)=1

foci

\frac{( x - 11 ) ^{2}}{63} + \frac{( y - 13 ) ^{2}}{81} = 1

(11, 13 + 32), (11, 13 - 32)

Solution steps

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

Calculate ellipse properties

\frac{( x - 11 ) ^{2}}{63} + \frac{( y - 13 ) ^{2}}{81} = 1 :

Ellipse with center

(h, k) = (11, 13), b = 9, a = 37

(11, 13 + c), (11, 13 - c)

Compute

c :

c = 9^{2} - (37)^{2} : 32

(11, 13 + 32), (11, 13 - 32)

\frac{( x - 7 ) ^{2}}{144} + \frac{( y - 4 ) ^{2}}{128} = 1

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

37 x^{2} + y^{2} = 37

\frac{( x - 1 ) ^{2}}{16} + \frac{( y - 4 ) ^{2}}{52} = 1

\frac{x ^{2}}{5} + \frac{y ^{2}}{4} = 1

What is the foci ((x-11)^2)/(63)+((y-13)^2)/(81)=1 ?
The foci ((x-11)^2)/(63)+((y-13)^2)/(81)=1 is (11,13+3sqrt(2)),(11,13-3sqrt(2))