What is the foci 9x^2+16y^2-36x+96y+36=0 ?

The foci 9x^2+16y^2-36x+96y+36=0 is (2+sqrt(7),-3),(2-sqrt(7),-3)

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foci 9x^2+16y^2-36x+96y+36=0

foci

9 x^{2} + 16 y^{2} - 36 x + 96 y + 36 = 0

(2 + 7, - 3), (2 - 7, - 3)

Solution steps

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

Calculate ellipse properties

9 x^{2} + 16 y^{2} - 36 x + 96 y + 36 = 0 :

Ellipse with center

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

(2 + c, - 3), (2 - c, - 3)

Compute

c :

c = 4^{2} - 3^{2} : 7

(2 + 7, - 3), (2 - 7, - 3)

\frac{( x - 1 ) ^{2}}{45} + \frac{y ^{2}}{54} = 1

36 x^{2} + 5 y^{2} - 90 y - 495 = 0

16 x^{2} - 32 x + 9 y^{2} = 128

(\frac{x ^{2}}{15}) + (\frac{y ^{2}}{16}) = 1

9 x^{2} - 18 x + 25 y^{2} - 250 y + 409 = 0

What is the foci 9x^2+16y^2-36x+96y+36=0 ?
The foci 9x^2+16y^2-36x+96y+36=0 is (2+sqrt(7),-3),(2-sqrt(7),-3)