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

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

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

foci

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

(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 = 0 :

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)

\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

4 x^{2} + 2 y^{2} + 2 x - 8 y + 7 = 0

9 x^{2} - 36 x + 4 y^{2} = 0

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