Given the ellipse 8x^2 + y^2 + 80x - 6y + 193 = 0 find: a)  The Center C b)  The Length of Major Axis c)  The Length of Minor Axis d)  Distance from C to foci

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The equation of the ellipse is 8x^2 + y^2 + 80x - 6y + 193 = 0

8x^2 + y^2 + 80x - 6y + 193 = 0

=> 8x^2 + 80x + y^2 - 6y + 193 = 0

=> 8(x^2 + 10x + 25) + y^2 - 6y + 9 = -193 + 200 + 9

=> 8(x^2 + 10x + 25) + y^2 - 6y + 9 = 16

=> `(x + 5)^2/(sqrt2)^2 + (y - 3)^2/4^2 = 1`

The center of the ellipse is (-5, 3). The length of the major axis is 8, The length of the minor axis is `2*sqrt 2` . The distance of the center from the foci is `sqrt 14`

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