What is the foci 16x^2-96x+4y^2=-80 ?

The foci 16x^2-96x+4y^2=-80 is (3,2sqrt(3)),(3,-2sqrt(3))

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foci 16x^2-96x+4y^2=-80

foci

16 x^{2} - 96 x + 4 y^{2} = - 80

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

Solution steps

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

Calculate ellipse properties

16 x^{2} - 96 x + 4 y^{2} = - 80 :

Ellipse with center

(h, k) = (3, 0), b = 4, a = 2

(3, 0 + c), (3, 0 - c)

Compute

c :

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

(3, 0 + 23), (3, 0 - 23)

Refine

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

3 x^{2} + y^{2} + 18 x - 2 y - 8 = 0

\frac{( x - 8 ) ^{2}}{49} + \frac{( y + 1 ) ^{2}}{100} = 1

\frac{( x - 1 ) ^{2}}{36} + \frac{( y + 2 ) ^{2}}{25} = 1

36 x^{2} + 9 y^{2} + 36 y - 288 = 0

100 x^{2} + 36 y^{2} = 225

What is the foci 16x^2-96x+4y^2=-80 ?
The foci 16x^2-96x+4y^2=-80 is (3,2sqrt(3)),(3,-2sqrt(3))