# A particle moves in x-y plane according to rule x = a sin ωt and y = a cosωt. The particle follows (1) An elliptical path (2) A circular path (3) A parabolic path (4) A straight line path inclined equally to x and y-axes

x2=a2sin2$w$t …............Eq(1)
y2=a2cos2$w$t ….............. Eq(2)
Eq (1) + Eq(2) $\Rightarrow$ x2+y2=awhich is a circles equation.