The method by which active food like Paramoecium is ingested by Amoeba proteus is circumvallation.

Explanation:
Amoeba proteus is a unicellular organism belonging to the phylum Protozoa. It is commonly found in freshwater environments and is known for its ability to engulf and consume food particles through a process called phagocytosis.

Phagocytosis is a form of endocytosis where the cell membrane surrounds and engulfs solid particles to form a food vacuole. In the case of Amoeba proteus, it feeds on small organisms such as bacteria, algae, and other protozoa.

The process of ingesting active food like Paramoecium involves several steps, with circumvallation being the specific method used by Amoeba proteus:

1. Detection and Recognition:
Amoeba proteus uses its sensitive and flexible pseudopodia extensions to detect and recognize potential food sources. It can sense the movement and presence of nearby organisms.

2. Contact and Adhesion:
Once a suitable prey, such as a Paramoecium, is detected, Amoeba proteus extends its pseudopodia towards the prey and makes contact. The pseudopodia surround and adhere to the surface of the prey.

3. Circumvallation:
Circumvallation is the process by which Amoeba proteus forms a circular membrane or "ring" around the prey, enclosing it within a pocket formed by the pseudopodia. This ring gradually contracts, tightening around the prey and creating a sealed enclosure.

4. Engulfment:
As the circular membrane contracts, the prey organism, in this case, Paramoecium, is engulfed within the pocket formed by the pseudopodia. The food vacuole, which contains digestive enzymes, is also formed during this process.

5. Digestion and Absorption:
Once the prey is fully engulfed within the food vacuole, the digestive enzymes are released to break down the prey into simpler molecules. The nutrients from the digested prey are then absorbed into the cytoplasm of the Amoeba proteus for energy and growth.

Conclusion:
In conclusion, Amoeba proteus ingests active food like Paramoecium through the process of circumvallation, where it forms a circular membrane around the prey using its pseudopodia. This method allows Amoeba proteus to efficiently capture and consume its food sources in its freshwater habitat.