hyperbole (n.)

"excessive or misleading publicity or advertising," 1967, American English (the verb is attested from 1937), probably in part a back-formation of hyperbole, but also from underworld slang verb hype "to swindle by overcharging or short-changing" (1926), itself a back-formation from hyper "short-change con man" (1914), from the prefix hyper- meaning "over, to excess."

Also possibly influenced by drug addicts' slang hype, shortening of hypodermic needle (1913). Related: Hyped; hyping. In early 18c., hyp "morbid depression of the spirits" was colloquial for hypochondria (usually as the hyp or the hyps).

curve formed by the intersection of a plane with a double cone, 1660s, from Latinized form of Greek hyperbole "extravagance," literally "a throwing beyond (others);" see hyperbole, which in English is the same word in its Greek garb. Perhaps so called because the inclination of the plane to the base of the cone exceeds that of the side of the cone.