Why did the ghost of the dead king appear to Hamlet?

that the ghost may be a figment of Hamlet’s imagination,

Explanation:

The ghost appears to Hamlet as his father, though alternate readings of the play allow for the possibilities that the ghost may be a figment of Hamlet’s imagination, a malevolent demon seeking to derail Hamlet’s life, or even an actor working on Claudius ’s behalf in an attempt to drive Hamlet mad and exclude him from the line of succession to the throne.