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Question

# The position of a particle moving in the x−y plane varies with time t as (dxdt)=8πsin2πt and (dydt)=5πcos2πt. When t=0,x=8,y=0. The path of the particle is

A
a straight line
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B
a circle
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C
an ellipse
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D
a parabola
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Solution

## The correct option is C an ellipsedx=8πsin2πtdt, on integration we get, x=−4cos2πt+cAtt=0,x=8soc=12(x−12)4=−cos2πt.......................................(1)Similarly, y=52sin2πt+cAtt=0,y=0soc=0y52=sin2πt...........................................(2)(x−12)216+4y225=1⇐Equationofellipse

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