C

Step 1: Understand the motion: When a particle moves with constant acceleration in a direction different from its initial velocity, it will undergo a change in its velocity vector over time.

Step 2: Analyze the effects of acceleration: Since the acceleration is constant but not in the direction of the initial velocity, the particle will not move in a straight line. Instead, the changing velocity will cause the trajectory to curve.

Step 3: Determine the type of path: The path will typically resemble a parabola because the component of acceleration perpendicular to the initial velocity causes a change in direction while the component along the direction of velocity causes a change in speed, leading to a parabolic trajectory.

Therefore, the answer is Option C: A parabola.