Question

can a tropical cyclone originate over a hot desert

Answer 1

 Tropical cyclones can only form over water. There is not enough hydrologic energy over a desert to begin the cyclonic action. 

Answer 2

No, tropical cyclones can only form over water.

The reason why this is is because the warm water helps circulate enough energy to create a tropical cyclone, and there isn't enough water in a desert to do so.