What is the foci 36x^2+9y^2+48x-36y+43=0 ?

The foci 36x^2+9y^2+48x-36y+43=0 is (-2/3 ,(4+sqrt(3))/2),(-2/3 ,(4-sqrt(3))/2)

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foci 36x^2+9y^2+48x-36y+43=0

foci

36 x^{2} + 9 y^{2} + 48 x - 36 y + 43 = 0

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

Solution steps

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

Calculate ellipse properties

36 x^{2} + 9 y^{2} + 48 x - 36 y + 43 = 0 :

Ellipse with center

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

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

Compute

c :

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

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

Refine

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

4 x^{2} + 9 y^{2} - 18 y - 27 = 0

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

\frac{( x - 4 ) ^{2}}{9} + (y + 3)^{2} = 1

2 x^{2} + 5 y^{2} = 10

x^{2} + 4 y^{2} - 2 x - 16 y + 13 = 0

What is the foci 36x^2+9y^2+48x-36y+43=0 ?
The foci 36x^2+9y^2+48x-36y+43=0 is (-2/3 ,(4+sqrt(3))/2),(-2/3 ,(4-sqrt(3))/2)