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)

16 (x - 4)^{2} + 25 (y + 2)^{2} = 400

\frac{x ^{2}}{38} + \frac{y ^{2}}{22} = 1

\frac{( x - 4 ) ^{2}}{25} + \frac{( y - 2 ) ^{2}}{16} = 1

14 x^{2} + 5 y^{2} - 70 = 0

\frac{( x - 4 ) ^{2}}{5 ^{2}} + \frac{( y - 1 ) ^{2}}{2 ^{2}} = 1

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)