b
\(\begin{array}{l}
\,\,\,\,\,\,\,\,\,\,x = a\,\sin \,\omega t\,\,\,or\,\frac{x}{a} = \sin \,\omega t\,\,\,\,\,...\left( i \right)\\
\,\,\,\,\,\,\,\,\,y = \,a\,\cos \,\omega t\,\,or\,\frac{y}{a} = \,\cos \,\omega t\,\,\,\,...\left( {ii} \right)\\
Squaring\,and\,adding,\,we\,get\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{a^2}}} = 1\,\,\,\left( {\,{{\cos }^2}\,\omega t + \sin \omega t = 1} \right)\\
or\,\,\,{x^2} + {y^2} = {a^2}\\
This\,is\,the\,equation\,of\,a\,circle.\,Hence\\
particle\,follows\,a\,circular\,path.
\end{array}\)