A) an elliptical path
B) a circular path
C) a parabolic path
D) a straight line path inclined equally to \[x\] and y-axes
Correct Answer: B
Solution :
\[x=a\sin \omega t\Rightarrow \frac{x}{a}=\sin \omega t\] \[x=a\cos \omega t\Rightarrow \frac{x}{{{a}^{2}}}=\cos \omega t\] \[\therefore \] \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] or \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\] This is equation of circle, so the particle follows a circular path.
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