If a line segment AM=a moves in the plane XOY remaining parallel to OX so that the left end point A slides along the circle x2+y2=a2, the locus of M is
A
x2+y2=4a2
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B
x2+y2=2ax
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C
x2+y2=2ay
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D
x2+y2−2ax−2ay=0
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Solution
The correct option is Bx2+y2=2ax Let the coordinates of A be (x,y) and M be (α,β)(Fig.16.13)
Since AM is parallel to OX
α=x+a and β=y⇒x=α−a and y=β
As A(x,y) lies on the circle x2+y2=a2 we have (α−a)2+β2=a2