The fat when burned to the energy, it releases many ketones in the blood and so urine. This process of producing energy by the fats is fat acid catabolism. Hence a large amount of the ketone gets eliminated in the urine causing ketonuria.
Related Theory
A condition in which abnormally high amounts of ketones and ketone bodies (a by product of the breakdown of cells) are present in the urine is called Ketonuria. It is a sign seen in extreme case of diabetes mellitus.