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Question

If P(x,y) divides the line segment joining A(5,0) and B(10cosθ,10sinθ) internally in the ratio 2:3, then which of the following is (are) true?

A
Distance of P from (3,0) is always constant.
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B
x[0,3]
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C
x2+y26x7=0
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D
y[4,0]
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Solution

The correct option is C x2+y26x7=0
By section formula,
(x,y)=(20cosθ+155,20sinθ+05)
=(4cosθ+3,4sinθ)
x=4cosθ+3,y=4sinθ

Since, cosθ and sinθ[1,1]
x[1,7] and y[4,4]

Distance of P from (3,0) is (x3)2+y2 =16sin2θ+16cos2θ=4, which is a constant.
(x3)2+y2=42
x2+y26x7=0


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