What is the foci 4x^2+y^2-16x-2y-19=0 ?

The foci 4x^2+y^2-16x-2y-19=0 is (2,1+3sqrt(3)),(2,1-3sqrt(3))

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foci 4x^2+y^2-16x-2y-19=0

foci

4 x^{2} + y^{2} - 16 x - 2 y - 19 = 0

(2, 1 + 33), (2, 1 - 33)

Solution steps

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

Calculate ellipse properties

4 x^{2} + y^{2} - 16 x - 2 y - 19 = 0 :

Ellipse with center

(h, k) = (2, 1), b = 6, a = 3

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

Compute

c :

c = 6^{2} - 3^{2} : 33

(2, 1 + 33), (2, 1 - 33)

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

3 x^{2} + 7 y^{2} = 63

25 x^{2} + 9 y^{2} = 225

\frac{x ^{2}}{34} + \frac{y ^{2}}{9} = 1

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

What is the foci 4x^2+y^2-16x-2y-19=0 ?
The foci 4x^2+y^2-16x-2y-19=0 is (2,1+3sqrt(3)),(2,1-3sqrt(3))