The definition of analytic geometry is solving geometry problems by representing geometric figures with algebraic equations and plotting them on a coordinate graphing system.
Coordinate geometry is an example of analytic-geometry.
the branch of geometry in which a coordinate graphing system makes visible, using points, lines, and curves, the numerical relationships of algebraic equations
also called coordinate geometry or Cartesian geometry
The analysis of geometric structures and properties principally by algebraic operations on variables defined in terms of position coordinates.