The incas burned the city of quito because

The Incas burned the city of Quito because they were defeated by the Spaniards. The Incas wanted to prevent their conquerors to take the city of Quito.

Explanation:

Here is some background information as regards the conquest of Quito:

Quito's history starts long before 1534, date of the Spanish foundation. The Incas conquered the highland part of what is now Ecuador and incorporated it into their empire by the end of the 15th century. Although pre-Hispanic traces disappeared with the conquistador's arrival, it has been said that before the Europeans arrived, Rumiñahui, an indigenous warrior, set the city on fire and destroyed the temples of the Incas who lived there.

The Inca ruled the Ecuadorian Kingdoms until the arrival of Francisco Pizarro, Diego de Almargo and a force of Spanish conquistadors in 1532. During the period of Inca control, the Ecuadorian tribesmen assimilated agricultural practices and the social organization of the Inca, but they maintained their traditional religious beliefs and many customs.

By the time the Spanish arrived in Ecuador in 1526, Quito was a major Inca city.  By mid-1534 the Spaniards had taken Quito and effectively defeated the Inca armies. Weakened by civil war and leaderless, the Inca empire collapsed swiftly. The Spanish conquest of Ecuador can be described as nothing less than brutal.

In 1533, rather than allowing it to fall into the hands of the Spanish conquerors, Rumiñahui, a general of Inca ruler Atahualpa, razed the city shortly before their arrival, destroying this ancient pre-Hispanic city to prevent the Spanish from taking it. There are no Inca remains.