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)

\frac{( x - 1 ) ^{2}}{5} + \frac{( y - 3 ) ^{2}}{4} = 1

\frac{2 x ^{2}}{25} + \frac{( y - 3 ) ^{2}}{49} = 1

\frac{( x - 3 ) ^{2}}{2} + \frac{( y - 5 ) ^{2}}{9} = 1

4 x^{2} + 81 y^{2} = 324

\frac{( x - 2 ) ^{2}}{9} + \frac{( y + 1 ) ^{2}}{4} = 1

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))