What is the foci 4x^2+36y^2-24x-288y+611=0 ?

The foci 4x^2+36y^2-24x-288y+611=0 is ((9+sqrt(2))/3 ,4),((9-sqrt(2))/3 ,4)

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foci 4x^2+36y^2-24x-288y+611=0

foci

4 x^{2} + 36 y^{2} - 24 x - 288 y + 611 = 0

(\frac{9 + 2}{3}, 4), (\frac{9 - 2}{3}, 4)

Solution steps

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

Calculate ellipse properties

4 x^{2} + 36 y^{2} - 24 x - 288 y + 611 = 0 :

Ellipse with center

(h, k) = (3, 4), a = \frac{1}{2}, b = \frac{1}{6}

(3 + c, 4), (3 - c, 4)

Compute

c :

c = (\frac{1}{2})^{2} - (\frac{1}{6})^{2} : \frac{2}{3}

(3 + \frac{2}{3}, 4), (3 - \frac{2}{3}, 4)

Refine

(\frac{9 + 2}{3}, 4), (\frac{9 - 2}{3}, 4)

\frac{( x - 1 ) ^{2}}{12} + \frac{( y - 2 ) ^{2}}{8} = 1

\frac{( x + 3 ) ^{2}}{4} + \frac{( y + 2 ) ^{2}}{16} = 1

1 x^{(2)} + 4 y^{(2)} + 10 x + 9 y - 10 = 0

64 x^{2} + 16 y^{2} = 1024

16 x^{2} + 36 y^{2} + 192 x - 288 y + 576 = 0

What is the foci 4x^2+36y^2-24x-288y+611=0 ?
The foci 4x^2+36y^2-24x-288y+611=0 is ((9+sqrt(2))/3 ,4),((9-sqrt(2))/3 ,4)