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Question

The locus of a point P which divides the line joining (1,0) and (2cosθ,2sinθ) internally in the ratio 2:3 for all θ ϵ R is

A
a straight line
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B
a circle
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C
a pair of straight line
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D
a parabola
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Solution

The correct option is A a circle
Given points A(1,0) and B(2cosθ,2sinθ)
Equation of line AB
AB:y=2sinθ2cosθ1(x1)(1)
Point P divides line AB in ratio 2:3 internally
By section formula
P(4cosθ+35,4sinθ5)
Let h=4cosθ+35 and k=4sinθ5

Distance of point P from A(1,0) is 2
By distance formula
(h1)2+(k)2=4
Here above equation represents circle

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