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Question

The eccentric angle of a point on the ellipse x26+y22=1 whose distance from the centre of the ellipse is 5, units is/are

A
π6
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B
3π6
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C
5π6
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D
11π6
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Solution

The correct option is D 11π6
Any point on the ellipse x26+y22=1 is P(6cosθ,2sinθ)

Now CP=6cos2θ+2sin2θ=5 where C is centre
6(1sin2θ)+2sin2θ=5
4sin2θ=1
sin2θ=14=(12)2
sinθ=nπ±(π6)
θ=π6,5π6,7π6,11π6
θ[o,2π)

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