What is the foci 4x^2+y^2-8x+4y-8=0 ?

The foci 4x^2+y^2-8x+4y-8=0 is (1,-2+2sqrt(3)),(1,-2-2sqrt(3))

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foci 4x^2+y^2-8x+4y-8=0

foci

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

(1, - 2 + 23), (1, - 2 - 23)

Solution steps

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

Calculate ellipse properties

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

Ellipse with center

(h, k) = (1, - 2), b = 4, a = 2

(1, - 2 + c), (1, - 2 - c)

Compute

c :

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

(1, - 2 + 23), (1, - 2 - 23)

25 x^{2} + 144 y^{2} = 900

3 x^{2} + 6 y^{2} = 18

x^{2} + y^{2} + 4 y = 0

4 x^{2} + 9 y^{2} - 8 x - 36 y + 4 = 0

16 x^{2} + 25 y^{2} + 32 x - 384 = 0

What is the foci 4x^2+y^2-8x+4y-8=0 ?
The foci 4x^2+y^2-8x+4y-8=0 is (1,-2+2sqrt(3)),(1,-2-2sqrt(3))