Given that we need to find the centre, lengths of axes, eccentricity and foci of the ellipse
3x2 + 4y2 - 12x - 8y + 4 = 0.
⇒ 3x2 + 4y2 - 12x - 8y + 4 = 0
⇒ 3(x2 - 4x + 4) + 4(y2 - 2y + 1) - 12 = 0
⇒ 3(x - 2)2 + 4(y - 1)2 = 12
Comparing with the standard form
⇒ Centre = (p, q) = (2,1)
Here a2 > b2
⇒ eccentricity(e) =
Length of the major axis 2a = 2(2) = 4
Length of the minor axis 2b = 2(√3) = 2√3
⇒ Foci = (p ± ae, q)
⇒ Foci = ((2 ± 1), 1)
⇒ Foci = (3,1) and (1,1)