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Question

A point on the ellipse x216+y29=1 at a distance equal to the mean of the lengths of the semi major axis and semi minor axis from the centre is

A
(±2917,±310514)
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B
(±2917,±31057)
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C
(±21057,±39114)
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D
(±210514,±39114)
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Solution

The correct option is A (±2917,±310514)
Length of semi major axis and semi minor axis of the ellipse x216+y29=1 are 4 and 3 respectively. So mean of these lengths is 72.

Let the coordinates of any point on the ellipse be P(4cosθ,3sinθ). If the distance of P from the centre(0,0) of the ellipse is 72, then 16cos2θ+9sin2θ=494
28cos2θ=13cosθ=±1328=±9114
and sinθ=±10514.

So, the coordinates of the required point are (±49114,±310514)
or (±2917,±310514)

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