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

Question

Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse: x 2 + 2y 2 - 2x + 12y + 10 = 0

Philoid · Accepted Answer

Given that we need to find the centre, lengths of axes, eccentricity and foci of the ellipse x² + 2y² - 2x + 12y + 10 = 0.

⇒ x² + 2y² - 2x + 12y + 10 = 0

⇒ (x² - 2x + 1) + 2(y² + 6y + 9) - 9 = 0

⇒ (x - 1)² + 2(y + 3)² = 9

⇒

Comparing with the standard form

⇒ Centre = (p,q) = (1, - 3)

Here a²>b²

⇒ eccentricity(e) =

⇒

Length of the major axis 2a = 2(3) = 6

Length of the minor axis 2b = = 3

⇒ Foci = (p±ae,q)

⇒ Foci =