Polar and Cartesian curves are two fundamental ways of describing geometric shapes, each based on a different coordinate system. In the Cartesian system, every point is described using a horizontal position and a vertical position, usually called x and y. Curves are often written as y depending on x, which makes this system especially useful for studying functions, slopes, and rates of change. Many familiar shapes, such as straight lines, parabolas, and circles, are naturally expressed in Cartes