What is the foci x^2+4y^2-6x+20y-2=0 ?

The foci x^2+4y^2-6x+20y-2=0 is (3+3sqrt(3),-5/2),(3-3sqrt(3),-5/2)

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foci x^2+4y^2-6x+20y-2=0

foci

x^{2} + 4 y^{2} - 6 x + 20 y - 2 = 0

(3 + 33, - \frac{5}{2}), (3 - 33, - \frac{5}{2})

Solution steps

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

Calculate ellipse properties

x^{2} + 4 y^{2} - 6 x + 20 y - 2 = 0 :

Ellipse with center

(h, k) = (3, - \frac{5}{2}), a = 6, b = 3

(3 + c, - \frac{5}{2}), (3 - c, - \frac{5}{2})

Compute

c :

c = 6^{2} - 3^{2} : 33

(3 + 33, - \frac{5}{2}), (3 - 33, - \frac{5}{2})

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

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

25 x^{2} + 144 y^{2} = 900

3 x^{2} + 6 y^{2} = 18

x^{2} + y^{2} + 4 y = 0

What is the foci x^2+4y^2-6x+20y-2=0 ?
The foci x^2+4y^2-6x+20y-2=0 is (3+3sqrt(3),-5/2),(3-3sqrt(3),-5/2)