What is the foci x^2-4x+100y^2+200y+4=0 ?

The foci x^2-4x+100y^2+200y+4=0 is (2+3sqrt(11),-1),(2-3sqrt(11),-1)

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foci x^2-4x+100y^2+200y+4=0

foci

x^{2} - 4 x + 100 y^{2} + 200 y + 4 = 0

(2 + 311, - 1), (2 - 311, - 1)

Solution steps

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

Calculate ellipse properties

x^{2} - 4 x + 100 y^{2} + 200 y + 4 = 0 :

Ellipse with center

(h, k) = (2, - 1), a = 10, b = 1

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

Compute

c :

c = 1 0^{2} - 1^{2} : 311

(2 + 311, - 1), (2 - 311, - 1)

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

\frac{( x - 9 ) ^{2}}{4} + \frac{( y + 10 ) ^{2}}{81} = 1

18 x^{2} + 8 y^{2} + 36 x - 32 y - 22 = 0

\frac{x ^{2}}{32} + \frac{y ^{2}}{9} = 1

4 x^{2} + 25 y^{2} - 24 x + 250 y + 561 = 0

What is the foci x^2-4x+100y^2+200y+4=0 ?
The foci x^2-4x+100y^2+200y+4=0 is (2+3sqrt(11),-1),(2-3sqrt(11),-1)