Question

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

x² + 4y² - 2x = 0

Answer 1

Given that we need to find the centre, lengths of axes, eccentricity and foci of the ellipse x² + 4y² - 2x = 0

⇒ x² + 4y² - 2x = 0

⇒ (x² - 2x + 1) + 4(y²) - 1 = 0

⇒ (x - 1)² + 4(y - 0)² = 1

Comparing with the standard form

⇒ Centre = (p, q) = (1, 0)

Here a² > b²

⇒ eccentricity(e) = 

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

Length of the minor axis 2b = 2\(\left(\cfrac12\right)\) = 1

⇒ Foci = (p ± ae, q)