In this page analytical geometry you can find many sub topics in this main topic. Rene Descartes (1596-2650) whose "La Geometric" was published in 1637 as an appendix to his "Discours de la methods" is regarded as the inventor as analytical geo-metry and modern analytical geometry is called Cartesian Geometry after him.
However the fundamental principles and methods of this topic were already discovered by Pierre de Fermat earlier.
Descartes procedure in geometry was to begin with a geometry problem to convert it into an algebraic equation simplify it and then solve the equation geometric.
However, even the usual formula for distance between two points, slope and angle between two straight lines are not to be found in this work of Decartes.
These are due to later mathematicians like Clairaut, Monge and Larcoin. Newton used several types of co-ordinates including polar and bipolar.L'Hospital had written a famous text book.