What is the foci x^2+3y^2-6x+6y=0 ?

The foci x^2+3y^2-6x+6y=0 is (3+2sqrt(2),-1),(3-2sqrt(2),-1)

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foci x^2+3y^2-6x+6y=0

foci

x^{2} + 3 y^{2} - 6 x + 6 y = 0

(3 + 22, - 1), (3 - 22, - 1)

Solution steps

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

Calculate ellipse properties

x^{2} + 3 y^{2} - 6 x + 6 y = 0 :

Ellipse with center

(h, k) = (3, - 1), a = 23, b = 2

(3 + c, - 1), (3 - c, - 1)

Compute

c :

c = (23)^{2} - 2^{2} : 22

(3 + 22, - 1), (3 - 22, - 1)

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

\frac{( x - 3 ) ^{2}}{16} + \frac{y ^{2}}{9} = 1

\frac{( x + 8 ) ^{2}}{169} + \frac{( y + 9 ) ^{2}}{25} = 1

9 x^{2} + 25 y^{2} + 36 x + 250 y = - 436

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

What is the foci x^2+3y^2-6x+6y=0 ?
The foci x^2+3y^2-6x+6y=0 is (3+2sqrt(2),-1),(3-2sqrt(2),-1)