A charged particle is deflected by two mutually perpendicular oscillating electric fields such that the displacement of the particle due to each one of them is given by x = A sin (ωt) and y = A sin (ωt+π6) respectively. The trajectory followed by the charged particle is

When two SHM's (which are perpendicular to each other ) are given by x=A1sinωt and y=A2sin(ωt+δ)  and when they are combined, the trajectory of the particle is given byx2A12+y2A22-2xyA1A2cosδ=sin2δ (This is equation of ellipse).For the given problem A1=A2=A and δ=π6,x2A2+y2A2-2xyA2.32=14x2+y2-3xy = 14A2 and this is an ellipse