Final answer:
The correct answer is catenary curve. A freely deforming cable under a uniformly distributed load assumes the shape of a catenary curve, which is distinct from parabolic, hyperbolic, or funicular curves.
Step-by-step explanation:
The shape assumed by a freely deforming cable or chain under the influence of a uniformly distributed load is known as a catenary curve. This curve is characteristic of flexible connectors such as cables or chains suspended from two points and subject only to their own weight. The catenary shape is different from a parabolic curve, which describes the trajectory of projectiles in a uniform gravitational field but without the effects of air resistance or the tension and flexibility found in cables.
A commonly observed example of a catenary curve is seen in power lines or the cables of a suspension bridge, where the cable takes on this natural form under the influence of gravity acting uniformly along its length. It is the curve that an idealized hanging cable or chain assumes under its own weight when supported only at its ends.