"the prince (king) is not regarded as a private person; he is a public personage, all the state is in him; the will of all the people is included in his. as all perfection and all strength are united in god, so all the power of individuals is united in (his) person." according to bossuet, what is the role of the king?

He believes the role of the king is to rule with complete authority over his subjects.
He compared the power of the king as the power of the God Himself. He believe that as long as the king is residing in His rightful nation/domain, all of His Desire would be met and all people within the nation/domain shall follow the King's order without hestitation.

The people of the kingdom look upon their king for everything. The king is the ruler. He is expected to look after the welfare of his people.As he has the power and resources to take care of the people of his kingdom . All the people support the king as he is expected to take care of their needs and deeds. As a king he should protect his people from outside invasion, provide them with good education system, provide healthcare.Encourage artist, sportsmen and intellectuals.