Step 1: Decode the term: orexigenic means appetite-promoting. The brain's appetite-driving peptides, orexin (hypocretin) and MCH, are synthesised by neurons whose somata sit in the lateral hypothalamic area.
Step 2: This region is the feeding centre. Lesions here reduce eating and produce wasting, whereas stimulation provokes overeating, matching the orexigenic label.
Step 3: The other choices are unrelated transmitter centres: dorsal raphe (serotonin), locus coeruleus (noradrenaline, arousal), and hippocampus (memory). None house orexin neurons.
\[\boxed{Lateral\ hypothalamic\ area}\]