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