What is the foci 9x^2-18x+4y^2=27 ?

The foci 9x^2-18x+4y^2=27 is (1,sqrt(5)),(1,-sqrt(5))

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foci 9x^2-18x+4y^2=27

foci

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

(1, 5), (1, - 5)

Solution steps

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

Calculate ellipse properties

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

Ellipse with center

(h, k) = (1, 0), b = 3, a = 2

(1, 0 + c), (1, 0 - c)

Compute

c :

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

(1, 0 + 5), (1, 0 - 5)

Refine

(1, 5), (1, - 5)

41 x^{2} + 16 y^{2} + 246 x - 192 y + 289 = 0

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

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

4 x^{2} + 25 y^{2} = 100

\frac{y ^{2}}{25} + \frac{x ^{2}}{9} = 1

What is the foci 9x^2-18x+4y^2=27 ?
The foci 9x^2-18x+4y^2=27 is (1,sqrt(5)),(1,-sqrt(5))