# 14.4: Analytic Geometry

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Analytic geometry is geometry within a coordinate system. While there are many coordinate systems here we will focus on just the three most used in academia: Cartesian (Rectangular), Cylindrical, and Spherical. There are others which we will mention later, but for now let us start with the conic sections.

• 14.4.1: Circles
A circle can be determined by fixing a point at the center and a positive number, the radius.
• 14.4.2: The Parabola
A parabola is the set of all points in a plane that are the same distance from a fixed line, called the directrix, and a fixed point (the focus) not on the directrix.
• 14.4.3: The Hyperbola
In analytic geometry, a hyperbola is a conic section formed by intersecting a right circular cone with a plane at an angle such that both halves of the cone are intersected. This intersection produces two separate unbounded curves that are mirror images of each other.
• 14.4.4: The Ellipse
This section is about another conic section, the ellipse. In this section, we will also investigate real-world applications, including how far apart two people in Statuary Hall can stand and still hear each other whisper.
• 14.4.5: Hyperbolic Functions
We were introduced to hyperbolic functions in Introduction to Functions and Graphs, along with some of their basic properties. In this section, we look at differentiation and integration formulas for the hyperbolic functions and their inverses.
• 14.4.6: Coordinate Systems
Coordinate systems allows us to make problems easier by picking the best coordinates for the job at hand. A coordinate system is a scheme that allows us to identify any point in the plane or in three-dimensional space by a set of numbers, but it also has uses in vector calculus with regards to divergence, gradient, curl, etc. The most common coordinate system is the Cartesian coordinates system. The two additional discussed here are cylindrical coordinates and spherical coordinates.

14.4: Analytic Geometry is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by LibreTexts.