I found a few different definitions online, none of which I found to be perfect, which I combined into "the representation of geometric objects and their positions and properties using coordinate systems and algebraic equations". Does anyone who's studied the subject have a better definition or a formal definition that isn't too complicated?
2026-04-22 06:15:30.1776838530
Best definition of analytic geometry
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Branches of mathematics do not have "formal definitions", they are defined by how people refer to them.
Your definition sounds fine.
I like to think of this historically: before Descartes we had "synthetic" geometry, i.e. axiomatic geometry in the style of Euclid; after Descartes we could model Euclid's geometry using numeric axes and that was the birth of "analytic" geometry.