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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 center is:

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

The correct option is A (2917,310514)
Given ellipse is x216+y29=1x242+y232=1
Length of semi-major and semi minor axes are 4 and 3 respectively.
So, the mean of these length is 72.
Let P(4cosθ,3sinθ) be a point on the ellipse at a distance 72 from the center (0,0).
16cos2θ+9sin2θ=49416cos2θ+9(1cos2θ)=494
28cos2θ=13cosθ=±1328=±9114 and sinθ=±10514

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

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