Yoga is not a fitness routine. It is an integration of the mind, body and spirit, and you will become fit by a diligent yoga practice, but by itself it does not reduce weight or ‘target” fat.
“Hot” or “Bikram” yoga will cause you to sweat, but that is not the same as losing weight from burning more calories than you consume. And there is controversy in the Yoga community over Bikram and whether it is a valid yoga practice.
“Core“is not a yoga term, but your core refers to your trunk, not your belly. A strong core is based on a total fitness of your abdomen, your back muscles, and your pectorals. Your core provides support and influences balance, so it is important to work on it. Cyclists and runners need to work on their core too, not just their legs. It is part of overall health.