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Question

If θ+π is the eccentric angle of a point on the ellipse 16x2+25y2=400, then the corresponding point on the auxilary circle is

A
(4cosθ,4sinθ)
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B
(5cosθ,5sinθ)
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C
(4cosθ,4sinθ)
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D
(5cosθ,5sinθ)
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Solution

The correct option is B (5cosθ,5sinθ)
Equation of the ellipse is:
16x2+25y2=400
x225+y216=1

Any point P(θ+π) on the ellipse can be written as (5cos(θ+π),4sin(θ+π)) or (5cosθ,4sinθ)

Hence corresponding point on the auxilary circle is (5cosθ,5sinθ)

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