The eccentric angle of a point on the ellipse x 2 + 3 y 2 = 6 lying at a distance of 2 units from its centre is

Step-by-step solution

The given equation of ellipse can be written in the form x 2 6 2 + y 2 2 2 = 1 . Now let the eccentric angle of the point be θ , then its co-ordinates are 6 cos θ , 2 sin θ . Since the distance of the point from the centre is 2 units ∴   6 cos θ - 0 2 + 2 sin θ - 0 2 = 4 ⇒ 6 cos 2 θ + 2 1 - cos 2 θ = 4 ⇒ 4 cos 2 θ = 2 ⇒     cos θ = ± 1 2         ∴     θ = π 4 or 3 π 4