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Find the eccentric angle of a point on t...

Find the eccentric angle of a point on the ellipse `(x^2)/6+(y^2)/2=1` whose distance from the center of the ellipse is `sqrt(5)`

Text Solution

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Let variable point on the ellipse `(x^(2))/(6)+(y^(2))/(2)=1 "be" p sqrt(6theta,sqrt(2)sin theta)`
Given that
`CP=sqrt(5)" "` (where C is centre)
`rArr sqrt (6 cos^(2)theta+2sin^(2)theta)=sqrt(5)`
`rArr 6(1sin^(2)theta)+2sin^(2)sin^(2)theta=5`
`rArr 4 sin^(2)theta=1`
`rArr sin theta= +-(1)/(2)`
`rArr theta =(pi)/(6),(5pi)/(6),(7pi)/(6),(11pi)/(6)`
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