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Question

A particle moves according to the equation x=asinωt and y=a(1cosωt) . The path of the particle is

A
circle
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B
parabola
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C
hyperbola
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D
cycloid
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E
ellipse
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Solution

The correct option is C cycloid
x=asinwt
y=a(1coswt)or(ya1)=coswt
(xa)2+(ya1)2=1
x2+(ya)2=a2 Equationofcircle
Thus the point moves on the rim of a circle which is above the origin by a, therefore the path traced by it is going to be cycloid.

202408_133837_ans.png

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