What is the foci x^2+4y^2-6x+16y+21=0 ?

The foci x^2+4y^2-6x+16y+21=0 is (3+sqrt(3),-2),(3-sqrt(3),-2)

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foci x^2+4y^2-6x+16y+21=0

foci

x^{2} + 4 y^{2} - 6 x + 16 y + 21 = 0

(3 + 3, - 2), (3 - 3, - 2)

Solution steps

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

Calculate ellipse properties

x^{2} + 4 y^{2} - 6 x + 16 y + 21 = 0 :

Ellipse with center

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

(3 + c, - 2), (3 - c, - 2)

Compute

c :

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

(3 + 3, - 2), (3 - 3, - 2)

\frac{x ^{2}}{64} + \frac{y ^{2}}{15} = 1

4 x^{2} + 24 x + 25 y^{2} + 200 y + 336 = 0

\frac{( x + 1 ) ^{2}}{10} + \frac{( y - 3 ) ^{2}}{9} = 1

\frac{( x ) ^{2}}{44} + \frac{y ^{2}}{125} = 1

2 x^{2} + 8 y^{2} = 16

What is the foci x^2+4y^2-6x+16y+21=0 ?
The foci x^2+4y^2-6x+16y+21=0 is (3+sqrt(3),-2),(3-sqrt(3),-2)