What is the foci 36x^2+16y^2-180x+96y-207=0 ?

The foci 36x^2+16y^2-180x+96y-207=0 is (5/2 ,-3+2sqrt(5)),(5/2 ,-3-2sqrt(5))

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foci 36x^2+16y^2-180x+96y-207=0

foci

36 x^{2} + 16 y^{2} - 180 x + 96 y - 207 = 0

(\frac{5}{2}, - 3 + 25), (\frac{5}{2}, - 3 - 25)

Solution steps

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

Calculate ellipse properties

36 x^{2} + 16 y^{2} - 180 x + 96 y - 207 = 0 :

Ellipse with center

(h, k) = (\frac{5}{2}, - 3), b = 6, a = 4

(\frac{5}{2}, - 3 + c), (\frac{5}{2}, - 3 - c)

Compute

c :

c = 6^{2} - 4^{2} : 25

(\frac{5}{2}, - 3 + 25), (\frac{5}{2}, - 3 - 25)

x^{2} + 2 y^{2} + 2 x - 4 y - 1 = 0

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

\frac{x ^{2}}{64} + \frac{y ^{2}}{1} = 1

\frac{x ^{2}}{16} + \frac{( y - 1 ) ^{2}}{36} = 1

\frac{( x + 2 ) ^{2}}{10} + \frac{( y - 5 ) ^{2}}{2} = 1

What is the foci 36x^2+16y^2-180x+96y-207=0 ?
The foci 36x^2+16y^2-180x+96y-207=0 is (5/2 ,-3+2sqrt(5)),(5/2 ,-3-2sqrt(5))