**Analytic geometry** creates a connection between graphs and equations. For example, the linear function f(x) = x^{2} – 2 (an equation) can also be represented by a graph:

Euclidean Geometry is based solely on geometric axioms without formulas or co-ordinates; **Analytic geometry is the “marriage” of algebra and geometry with axes and co-ordinates** [1].

## Calculus and Analytic Geometry

Calculus and analytic geometry have become so intertwined, it’s rare nowadays to find a course in pure “Analytic Geometry”. It’s more common to take a course in Calculus *and* Analytic Geometry, which blends the principles of basic analytic geometry with concepts like functions, limits, continuity, derivatives, antiderivatives, and definite integrals.

## Topics in Analytic Geometry A to Z

**Arc Length Formula**: An “arc” is a curve segment; The arc length formula tells you how long this segment is.**Area of a Bounded Region**: are of a shape contained within a set of functions.**Area under the curve**: Calculating the area between a graph and the x-axis.**Centroid**: The average of all points in an object (e.g. the center of volume or mass).**Center function**: gives the trilinear coordinates of a triangle’s center.**Distance Formula / Function**: measures the distance between two points in a set (e.g. on a line).**Delta x / Delta y**: Distance traveled along the x- or y-axis.**Displacement Function**: gives us how far a particle has moved from a starting point at an given time.**Distance Traveled**(using derivatives).**Intersection of lines**: The place where two or more graphs cross each other.**Length of a Line Segment**: Measuring “how far” along an x or y axis.**Parabola**: a u-shaped curve; The graph of a quadratic function.**Parallel Cross Sections**: repeated cross sections for a solid, parallel to each other.**Polar coordinates**: “Circular” coordinates on a plane.**Rate of change**: a measure (a rate) of how things are changing.**Slope**: the ratio of a change in x (δx) to a change in y (δy).**Quadrant**: one of the four regions of the Cartesian plane / x-y axis.**Riemann Sums**: Estimating the area under a curve with rectangles.**Secant line**: A secant line connects two ore more points on a curve; An external secant is the “outside” part of the secant line.**Sketching Graphs on the Cartesian Plane**.**Spherical coordinates**: Coordinate system on a sphere.**Tangent line**: a line that touches a graph at only one point and is practically parallel. See also: Vertical Tangents and Horizontal Tangents.**Tautochrone Problem / Brachistochrone**: Classic problems about swinging pendulums.**Testing for Symmetry of a Function**.**Transformations**: shifts, dilations and other “movement” along the x or y axis.**Vectors**: show magnitude and direction.**Velocity**: Rate of change of displacement.**x, y coordinate system:**A system with a horizontal (x) axis and vertical (y) axis.**x and y intercepts**: The points where a graph crosses the x-axis or y-axis.

## References

[1] Analytic Geometry and Calculus. Retrieved May 3, 2021 from: math.uci.edu/~ndonalds/math184/analytic.pdf

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