Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse:

3x² + 4y² - 12x - 8y + 4 = 0

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

⇒ Foci = (p±ae,q)

⇒ Foci =

⇒ Foci =

⇒ Foci = (3,1) and (1,1)