Explanations about the scope of the contents covered in the course, as well as by the topics of each of its chapters.


Chapter 1

Basic Elements of Analytical Geometry


Cartesian System of One Dimension

Cartesian System of Two Dimensions

Quadrants of the Cartesian System of Two Dimensions


Chapter 2

Straight Line Equations

General and Slope-Intercept Forms

General Equation

Slope-Intercept Equation

Slope Parameter and Linear Parameter of Slope-Intercept Equation

Slope-Intercept Equations from Two Points of the Straight Line

Slope-Intercept Equation from Angular and Linear Coefficient

Coordinates of the Points from Slope-Intercept Equation


Chapter 3

Straight Line Equations

Intercept-Intercept and Normal and Normalized Forms

Intercept-Intercept Equation of Straight Line

Obtaining the General and Slope-Intercept Equation from the Intercept-Intercept Equation

Normal Equation of Straight Line

Normal and Normalized Equations from General Equation of the Straight Line

General Equation from Normal Equation of Straight Line


Chapter 4

Straight Line Equations

Parametric Equation and Trigonometric Ratio Equation

Parametric Equation

Verification of the Parametric Equations

Trigonometric Ratio Equation

Trigonometric Ratio Equation from General Equation of Straight Line


Chapter 5

Important Relationships between Straight Lines (Part 1)

Equation of Straight Lines that pass through a Point

Straights Lines that Pass by Two Points

Equation of the Line that Pass through a Point and forms a Determined Angle with the x-axis

Division of a Line Segment into a Given Ratio

Distance between Two Points

Point of Intersection of Two Straight Lines

Parallel Straight Lines

Congruent Straight Lines

Collinear Points


Chapter 6

Important Relationships between Straight Lines (Part 2)

Angle between Two Straight Lines

Condition for Two Straight Lines to be Parallels

Condition for Two Concurrent Straight Lines being Perpendicular to Each Other

Distance from a Point to a Line

Bisector Line of the Angle formed by Two Concurrent Straight Lines

Bisectors Lines of Angles of a Triangle


Chapter 7

Circumference and Conic Curves

General Equation of Circumference

Intersection of Straight Lines and Circumferences

Conic Curves

Ellipse Equation

Hyperbola Equation

Parabola Equation