The path traced by a person standing at the middle of a slipping ladder would indeed be a circular path. To understand why other options are incorrect, let`s examine each:

Option 1: A straight line implies that the person would move either vertically or horizontally, which won`t happen because the ladder`s top is slipping down the wall and the bottom is slipping out.

Option 2: An elliptical path implies that the person`s motion has two different principal radii - a major and a minor radius. However, the pivot point, at the point where the ladder touches the wall and the movement of the person, maintains a constant radius.

Option 4: A parabolic path is associated with freely falling objects under gravity or projectile motion. But, the person here is not under such conditions.

Hence, a circular path (Option 3) illustrates the person`s motion accurately. Here, the point of contact between the wall and ladder acts as the pivot, and the mid-point of the ladder traces a half-circle as the ladder falls.