What is the foci 81x^2+16y^2=1296 ?

The foci 81x^2+16y^2=1296 is (0,sqrt(65)),(0,-sqrt(65))

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foci 81x^2+16y^2=1296

foci

81 x^{2} + 16 y^{2} = 1296

(0, 65), (0, - 65)

Solution steps

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

Calculate ellipse properties

81 x^{2} + 16 y^{2} = 1296 :

Ellipse with center

(h, k) = (0, 0), b = 9, a = 4

(0, 0 + c), (0, 0 - c)

Compute

c :

c = 9^{2} - 4^{2} : 65

(0, 0 + 65), (0, 0 - 65)

Refine

(0, 65), (0, - 65)

25 x^{2} + 9 y^{2} - 100 x - 90 y + 100 = 0

5 x^{2} + 7 y^{2} - 35 = 0

4 (x - 1)^{2} + 13 (y + 3)^{2} = 52

x^{2} + 5 y^{2} - 4 x + 20 y = - 19

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

What is the foci 81x^2+16y^2=1296 ?
The foci 81x^2+16y^2=1296 is (0,sqrt(65)),(0,-sqrt(65))