What is the foci x^2+2y^2+2x-20y+43=0 ?

The foci x^2+2y^2+2x-20y+43=0 is (1,5),(-3,5)

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foci x^2+2y^2+2x-20y+43=0

foci

x^{2} + 2 y^{2} + 2 x - 20 y + 43 = 0

(1, 5), (- 3, 5)

Solution steps

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

Calculate ellipse properties

x^{2} + 2 y^{2} + 2 x - 20 y + 43 = 0 :

Ellipse with center

(h, k) = (- 1, 5), a = 22, b = 2

(- 1 + c, 5), (- 1 - c, 5)

Compute

c :

c = (22)^{2} - 2^{2} : 2

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

Refine

(1, 5), (- 3, 5)

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

2 x^{2} + 3 y^{2} + 10 x + 10 y - 10 = 0

\frac{( x - 4 ) ^{2}}{9} + \frac{( y + 6 ) ^{2}}{4} = 1

\frac{x ^{2}}{16} + \frac{( y - 2 ) ^{2}}{9} = 1

\frac{( x + 4 ) ^{2}}{225} + \frac{( y - 7 ) ^{2}}{81} = 1

What is the foci x^2+2y^2+2x-20y+43=0 ?
The foci x^2+2y^2+2x-20y+43=0 is (1,5),(-3,5)