What is the foci 9x^2+4y^2-18x-16y-11=0 ?

The foci 9x^2+4y^2-18x-16y-11=0 is (1,2+sqrt(5)),(1,2-sqrt(5))

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foci 9x^2+4y^2-18x-16y-11=0

foci

9 x^{2} + 4 y^{2} - 18 x - 16 y - 11 = 0

(1, 2 + 5), (1, 2 - 5)

Solution steps

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

Calculate ellipse properties

9 x^{2} + 4 y^{2} - 18 x - 16 y - 11 = 0 :

Ellipse with center

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

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

Compute

c :

c = 3^{2} - 2^{2} : 5

(1, 2 + 5), (1, 2 - 5)

\frac{( x - 1 ) ^{2}}{36} + \frac{( y - 2 ) ^{2}}{115} = 3

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

\frac{( x - 3 ) ^{2}}{100} + \frac{( y - 1 ) ^{2}}{64} = 1

25 x^{2} + y^{2} - 4 y - 21 = 0

16 x^{2} + 25 y^{2} - 64 x + 150 y = - 279

What is the foci 9x^2+4y^2-18x-16y-11=0 ?
The foci 9x^2+4y^2-18x-16y-11=0 is (1,2+sqrt(5)),(1,2-sqrt(5))