When the bar makes an angle θ, the height of its COM (mid-point) is 2L​cosθ.∴ Displacement =L−2L​cosθ=2L​(1−cosθ)Since, forces on the rod are only along the vertical direction ( mg at C and N at B ), hence COM will fall vertically downwards. Instantaneous torque about point of contact isτ=mg×2L​sinθ or τ∝sinθNow, x=2L​sinθ;y=Lcosθ(L/2)2x2​+L2y2​=1Path of A is an ellipse.