Question

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

4x² + y² - 8x + 2y + 1 = 0

Answer 1

Given that we need to find the centre, lengths of axes, eccentricity and foci of the ellipse

4x² + y² - 8x + 2y + 1 = 0.

⇒ 4x² + y² - 8x + 2y + 1 = 0

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

⇒ 4(x - 1)² + (y + 1)² = 4

Comparing with the standard form

⇒ Centre = (p, q) = (1, - 1)

Here b² > a²

⇒ eccentricity(e) =

Length of the major axis 2b = 2(2) = 4

Length of the minor axis 2a = 2(1) = 2

⇒ Foci = (p, q ± be)