analytic geometry vs geometry

analytic geometry and geometry both are nouns.

Word	Noun	Adjective	Verb	Adverb
analytic geometry	Yes	No	No	No
geometry	Yes	No	No	No

As nouns, geometry is a hypernym of analytic geometry; that is, geometry is a word with a broader meaning than analytic geometry:

analytic geometry: the use of algebra to study geometric properties; operates on symbols defined in a coordinate system
geometry: the pure mathematics of points and lines and curves and surfaces

analytic geometry (noun)	geometry (noun)
the use of algebra to study geometric properties; operates on symbols defined in a coordinate system	the pure mathematics of points and lines and curves and surfaces