What is the foci 2x^2+4y^2+8x+9y-3=0 ?

The foci 2x^2+4y^2+8x+9y-3=0 is ((-16+sqrt(257))/8 ,-9/8),((-16-sqrt(257))/8 ,-9/8)

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foci 2x^2+4y^2+8x+9y-3=0

foci

2 x^{2} + 4 y^{2} + 8 x + 9 y - 3 = 0

(\frac{- 16 + 257}{8}, - \frac{9}{8}), (\frac{- 16 - 257}{8}, - \frac{9}{8})

Solution steps

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

Calculate ellipse properties

2 x^{2} + 4 y^{2} + 8 x + 9 y - 3 = 0 :

Ellipse with center

(h, k) = (- 2, - \frac{9}{8}), a = \frac{257}{4 2}, b = \frac{257}{8}

(- 2 + c, - \frac{9}{8}), (- 2 - c, - \frac{9}{8})

Compute

c :

c = (\frac{257}{4 2})^{2} - (\frac{257}{8})^{2} : \frac{257}{8}

(- 2 + \frac{257}{8}, - \frac{9}{8}), (- 2 - \frac{257}{8}, - \frac{9}{8})

Refine

(\frac{- 16 + 257}{8}, - \frac{9}{8}), (\frac{- 16 - 257}{8}, - \frac{9}{8})

36 x^{2} + 4 y^{2} + 360 x - 32 y + 820 = 0

\frac{( x - 1 ) ^{2}}{100} + \frac{( y - 2 ) ^{2}}{36} = 1

\frac{( x + 6 ) ^{2}}{4} + \frac{( y + 6 ) ^{2}}{25} = 1

\frac{( x + 2 ) ^{2}}{25} + \frac{( y - 5 ) ^{2}}{9} = 1

\frac{( x + 4 ) ^{2}}{24} + \frac{( y + 2 ) ^{2}}{49} = 1

What is the foci 2x^2+4y^2+8x+9y-3=0 ?
The foci 2x^2+4y^2+8x+9y-3=0 is ((-16+sqrt(257))/8 ,-9/8),((-16-sqrt(257))/8 ,-9/8)