Which of the following phrases correctly uses an infinitive?

The phrase "My goal is to run a marathon" correctly uses an infinitive. An infinitive is the base form of a verb preceded by "to." In this case, "to run" serves as the infinitive, expressing the intention or goal of the subject. This structure effectively conveys the purpose behind the goal.

In contrast, the other phrases misuse the concept of the infinitive or do not contain one. The first option uses "to dance" incorrectly following the verb "enjoys," as it should be followed by the gerund form "dancing." The third option, "I love swimming in the ocean," features "swimming," which is also a gerund rather than an infinitive. Lastly, while "He plans to finish his project" does contain an infinitive ("to finish"), the question specifically highlights the second option as the one that stands out among the choices for referring directly to a personal goal or objective with that clear use of the infinitive structure.