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Q.

A particle is moving in XY-plane whose x and y-coordinates are x=3sin⁡2πt and y=2cos⁡2πt, where, x and y are in metre and t is in second.

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a

The path of the particle is parabolic

b

The path of the particle is circular

c

The path of the particle is elliptical

d

The path of the particle is straight line

answer is A.

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Detailed Solution

∵x=3sin⁡2πt  or  x3=sin⁡2πt

and y2=cos⁡2πt

∴ sin2⁡2πt+cos2⁡2πt=x29+y24∴x29+y24=1

Thus, particle is moving on elliptical path.

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