What is the foci 16x^2+4y^2+96x-24y+116=0 ?

The foci 16x^2+4y^2+96x-24y+116=0 is (-3,3+2sqrt(3)),(-3,3-2sqrt(3))

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foci 16x^2+4y^2+96x-24y+116=0

foci

16 x^{2} + 4 y^{2} + 96 x - 24 y + 116 = 0

(- 3, 3 + 23), (- 3, 3 - 23)

Solution steps

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

Calculate ellipse properties

16 x^{2} + 4 y^{2} + 96 x - 24 y + 116 = 0 :

Ellipse with center

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

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

Compute

c :

c = 4^{2} - 2^{2} : 23

(- 3, 3 + 23), (- 3, 3 - 23)

\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1

\frac{( x ^{2} )}{16} + \frac{( y ^{2} )}{36} = 1

x^{2} + 4 y^{2} + 10 x + 8 y - 3 = 0

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

\frac{( x + 1 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{25} = 1

What is the foci 16x^2+4y^2+96x-24y+116=0 ?
The foci 16x^2+4y^2+96x-24y+116=0 is (-3,3+2sqrt(3)),(-3,3-2sqrt(3))