If eccentric angle of a point on the ellipse `x^(2)/6+y^(2)/2=1`, whose distance from the centre of ellipse is 2, is

Options

A. `pi//4`
B. `3pi//2`
C. `5pi//3`
D. `7pi//6`

Answer

A

Explanation

Let `theta` be the accentric angle of the point P. Then, the coordinates of P are `(sqrt(6) cos theta, sqrt(2) sin theta)`.
The centre of the ellipse is at the origin. It is given that OP = 2
`therefore OP = 2`
`rArr sqrt(6 cos^(2) theta + 2 sin^(2) theta = 2)`
`rArr 6 cos^(2) theta + 2 sin^(2) theta = 4`
`rArr 3 cos^(2) theta + sin^(2) theta = 2`
`rArr 2 sin^(2)theta = 1 rArr sin^(2)theta = 1/2 rArr sin theta = pm (1)/(sqrt2) rArr theta = pm pi//4`