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

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

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

foci

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

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

Solution steps

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

Calculate ellipse properties

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

Ellipse with center

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

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

Compute

c :

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

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

f (x) = x^{2} - 2 x + 3

9 x^{2} + 16 y^{2} = 144

9 x^{2} + 4 y^{2} = 36

f (x) = x^{2} + 5

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

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