The line segment joining (5,0) and (10cosθ,10sinθ) is divided internally in the ratio 2:3 at P. If θ varies, then the locus of P is
A
a pair of straight lines
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B
a circle
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C
a straight line
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D
a parabola
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E
an ellipse
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Solution
The correct option is B a circle Let the coordinates of point P be (x,y). Then, ⇒x=20cosθ+155 and y=20sinθ+05 ⇒x=4cosθ+3 and y=4sinθ ⇒x−3=4cosθ and y=4sinθ ⇒(x−3)2+y2=16 which is an equation of a circle.