Analytic Geometry

Description:

        Equations of lines and conic sections; curve tracing in both rectangular and polar coordinates in two-dimensional space.

Overview:

        In classical mathematics, analytic geometry is also known as coordinate geometry or Cartesian geometry. It is the study of geometry using a coordinate system. It is a branch of algebra that is used to model geometric objects - points, (straight) lines, and circles being the most basic of these. This contrasts with synthetic geometry. Analytic geometry is used in physics and engineering, and also in aviation, rocketry, space science, and spaceflight.

        The fundamental concepts of analytic geometry are the simplest geometric elements (points, straight lines, planes, second-order curves, and surfaces). The principal means of study in analytic geometry is the method of coordinates and the methods of elementary algebra.

        René Descartes and Pierre de Fermat independently founded analytic geometry in the 1630s by adapting Viète's algebra to the study of geometric loci.

Read More:
(1) Analytic geometry - Wikipedia

(2) Analytic geometry | Britannica

(3) What Is Analytic Geometry? - Cut the Knot

(4) Analytic geometry - Encyclopedia of Mathematics

(5) Analytic Geometry (Coordinate Geometry) Formulas - Byjus

Watch:
(1) Introduction to Coordinate Geometry | Geometry | Letstute
     by Letstute [4:49] | YouTube

(2) mathtalk- analytic geometry intro

      by mathtalkca [11:29] | YouTube

(3) Coordinate Geometry, Basic Introduction, Practice Problems
      by The Organic Chemistry Tutor [33:02] | YouTube

(4) ANALYTICAL GEOMETRY - The basics (a compilation)
       by The Maths Shack [33:19] | YouTube

(5) Pre-Calculus Introduction to Conic Sections and Analyzing Parabola in

      Filipino

       by Numberbender [11:07] | YouTube

Topics:

1. Plane Analytic Geometry
        a. The Cartesian Planes
        b. Distance Formula
        c. Point-of-Division Formulas
        d. Inclination and Slope
        e. Parallel and Perpendicular Lines
        f. Angle from One Line to Another
        g. An Equation of a Locus

2. The Line
        a. Point-Slope and Two-Point Forms
        b. Slope-Intercept and Intercept Forms
        c. Distance from a Point to a Line
        d. Normal Form

3. The Circle
        a. The Standard Form for an Equation of a Circle
        b. Conditions to Determine a Circle

4. Conic Sections
        a. Introduction to Conic Sections
        b. The Parabola
        c. The Ellipse
        d. The Hyperbola

5. Transformation of Coordinates
        a. Translation of Conic Sections

6. Curve Sketching
        a. Symmetry and Intercepts
        b. Sketching Polynomial Equations
        c. Asymptotes (Except Slant Asymptotes)
        d. Sketching Rational Functions

7. Polar Coordinates
        a. Polar Coordinates
        b. Graphs in Polar Coordinates
        c. Relationships Between Rectangular and Polar Coordinates

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