What is the foci (x+2)^2+((y+4)^2)/(1/4)=1 ?

The foci (x+2)^2+((y+4)^2)/(1/4)=1 is ((-4+sqrt(3))/2 ,-4),((-4-sqrt(3))/2 ,-4)

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foci (x+2)^2+((y+4)^2)/(1/4)=1

foci

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

(\frac{- 4 + 3}{2}, - 4), (\frac{- 4 - 3}{2}, - 4)

Solution steps

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

Calculate ellipse properties

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

Ellipse with center

(h, k) = (- 2, - 4), a = 1, b = \frac{1}{2}

(- 2 + c, - 4), (- 2 - c, - 4)

Compute

c :

c = 1^{2} - (\frac{1}{2})^{2} : \frac{3}{2}

(- 2 + \frac{3}{2}, - 4), (- 2 - \frac{3}{2}, - 4)

Refine

(\frac{- 4 + 3}{2}, - 4), (\frac{- 4 - 3}{2}, - 4)

16 x^{2} + 25 y^{2} - 128 x + 150 y + 81 = 0

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

16 x^{2} + 25 y^{2} - 96 x - 256 = 0

\frac{( ( x + 7 ) ^{2} )}{9} + \frac{( ( y - 4 ) ^{2} )}{7} = 1

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

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