What is the foci x^2+4y^2-6x+8y+9=0 ?

The foci x^2+4y^2-6x+8y+9=0 is (3+sqrt(3),-1),(3-sqrt(3),-1)

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foci x^2+4y^2-6x+8y+9=0

foci

x^{2} + 4 y^{2} - 6 x + 8 y + 9 = 0

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

Solution steps

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

Calculate ellipse properties

x^{2} + 4 y^{2} - 6 x + 8 y + 9 = 0 :

Ellipse with center

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

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

Compute

c :

c = 2^{2} - 1^{2} : 3

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

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

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

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

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

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

What is the foci x^2+4y^2-6x+8y+9=0 ?
The foci x^2+4y^2-6x+8y+9=0 is (3+sqrt(3),-1),(3-sqrt(3),-1)