What is the foci 81x^2-1296x+16y^2+64y=-3952 ?

The foci 81x^2-1296x+16y^2+64y=-3952 is (8,-2+sqrt(65)),(8,-2-sqrt(65))

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foci 81x^2-1296x+16y^2+64y=-3952

foci

81 x^{2} - 1296 x + 16 y^{2} + 64 y = - 3952

(8, - 2 + 65), (8, - 2 - 65)

Solution steps

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

Calculate ellipse properties

81 x^{2} - 1296 x + 16 y^{2} + 64 y = - 3952 :

Ellipse with center

(h, k) = (8, - 2), b = 9, a = 4

(8, - 2 + c), (8, - 2 - c)

Compute

c :

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

(8, - 2 + 65), (8, - 2 - 65)

x^{2} + 8 y^{2} = 32

25 x^{2} + y^{2} - 100 x + 8 y + 91 = 0

9 x^{2} + 36 y^{2} = 324

\frac{( x - 12 ) ^{2}}{289} + \frac{( y - 3 ) ^{2}}{64} = 1

9 X^{2} + 4 Y^{2} = 36

What is the foci 81x^2-1296x+16y^2+64y=-3952 ?
The foci 81x^2-1296x+16y^2+64y=-3952 is (8,-2+sqrt(65)),(8,-2-sqrt(65))