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)

81 x^{2} - 1296 x + 16 y^{2} + 64 y = - 3952

x^{2} + 8 y^{2} = 32

25 x^{2} + y^{2} - 100 x + 8 y + 91 = 0

9 x^{2} + 36 y^{2} = 324

\frac{( x - 12 ) ^{2}}{289} + \frac{( y - 3 ) ^{2}}{64} = 1

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)