Q1 of 76 Page 26

For the ellipse 12x2 + 4y2 + 24x – 16y + 25 = 0

Given that we need to find the centre, lengths of axes, eccentricity and foci of the ellipse 12x2 + 4y2 + 24x - 16y + 25 = 0.



⇒ 12x2 + 4y2 + 24x - 16y + 25 = 0


⇒ 12(x2 + 2x + 1) + 4(y2 - 4y + 4) - 3 = 0


⇒ 12(x + 1)2 + 4(y - 2)2 = 3


⇒


⇒


Comparing with the standard form


⇒ Centre = (p,q) = (1, - 2)


Here b2>a2


⇒ eccentricity(e) =


⇒


⇒


⇒


Length of the major axis 2b =


Length of the minor axis 2a = = 1


∴ The correct option is D

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