The distance of a point, P,on the ellpise ` x^(2)+3y^(2)=6` lying in the firsrt quadrant, form the centre of the ellipse is 2 units. The eccerntric angle of the point P is-

Options

A. `(pi)/(3)`
B. `(pi)/(4)`
C. `(pi)/(6)`
D. none of these

Answer

B

Explanation

Let `p(sqrt(6costheta),sqrt(2sintheta) )` be a point on the ellips
`(x^(2))/(6)+(y^(2))/(2)=1` in the first -quadrant `(thetaltthetalt(pi)/(2))`
`CP^(2)=6cos^(2)theta+2sin^(2)theta=4`
`rArr 2+ 4 cos^(2)theta=4`
`rArr cos^(2)theta=(1)/(2)`
`rArr cos theta=(1)/(sqrt(2))`
`rArr=(pi)/(4)`