What is the foci x^2+9y^2-8x+18y-11=0 ?

The foci x^2+9y^2-8x+18y-11=0 is (4+4sqrt(2),-1),(4-4sqrt(2),-1)

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foci x^2+9y^2-8x+18y-11=0

foci

x^{2} + 9 y^{2} - 8 x + 18 y - 11 = 0

(4 + 42, - 1), (4 - 42, - 1)

Solution steps

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

Calculate ellipse properties

x^{2} + 9 y^{2} - 8 x + 18 y - 11 = 0 :

Ellipse with center

(h, k) = (4, - 1), a = 6, b = 2

(4 + c, - 1), (4 - c, - 1)

Compute

c :

c = 6^{2} - 2^{2} : 42

(4 + 42, - 1), (4 - 42, - 1)

4 x^{2} + 36 y^{2} - 24 x - 288 y + 611 = 0

\frac{( x - 1 ) ^{2}}{12} + \frac{( y - 2 ) ^{2}}{8} = 1

\frac{( x + 3 ) ^{2}}{4} + \frac{( y + 2 ) ^{2}}{16} = 1

1 x^{(2)} + 4 y^{(2)} + 10 x + 9 y - 10 = 0

64 x^{2} + 16 y^{2} = 1024

What is the foci x^2+9y^2-8x+18y-11=0 ?
The foci x^2+9y^2-8x+18y-11=0 is (4+4sqrt(2),-1),(4-4sqrt(2),-1)