Final answer:
The lighting fixture that meets the criteria of utilizing gobos, functioning as a followspot, and having adjustable focal length with barrels is the Ellipsoidal reflector spotlight (ERS).
Step-by-step explanation:
The light fixture that can utilize gobos and templates, be used as a followspot, and can alter the focal length of the beam with the use of barrels is the Ellipsoidal reflector spotlight (ERS).
This type of lighting fixture is equipped with lenses and a reflector that allow it to shape light in various ways and project patterns or colors using gobos. It also has a mechanism to adjust the focus, making the beam sharper or softer. The flexibility in beam shaping and the ability to use gobos make the ERS a versatile tool in theatrical lighting and other applications that require precise lighting control.