Chapter 18: Introduction to Analytic Geometry

18.1: Introduction

1. Cartesian Coordinate System & Cartesian Plane
2. Derivation of Distance formula
3. Use of Distance formula
4. Problem 1: Use of Distance formula
5. Points Dividing the Join of Two Points in Given Ratio
6. More on Points Dividing Join of Two Points in Given Ratio
7. Problem1a-Points Dividing the Join of Two Points in Given Ratio
8. Problem1b-Points Dividing the Join of Two Points in Given Ratio

18.2: Translation and Rotation of Axes

1. Translation of Axes
2. Problem1-Translation of Axes
3. Problem2-Translation of Axes
4. Rotation of Axes
5. Problem1-Rotation of Axes
6. Problem2-Rotation of Axes

18.3: Equations of Straight Lines

1. Inclination of Line
2. Problem1-Inclination of Line
3. Slope or Gradient of a Line
4. Gradient of a Straight Line Joining Two Points
5. Slope of Collinear Line Segments
6. Slope of Parallel Lines
7. Problem-Slope of Parallel Lines
8. Problem2-Slope of Parallel Lines
9. Equations of a Straight Line
10. More on Equations of Straight Line
11. Problem-Equations of a Straight Line
12. Derivation of Slope Intercept form
13. Problem1-Derivation of Slope Intercept form
14. Deriving Point-slope Form of Equation of Straight Line
15. Problem1-Deriving Point-slope Form of Equation of Straight Line
16. Symmetric Form of Equation of Straight Line
17. Problem1-Symmetric Form of Equation of Straight Line
18. Two Point form of Equation of Straight Line
19. Problem1-Two Point form of Equation of Straight Line
20. Intercept Form of Equation of Straight Line
21. Problem1-Intercept Form of Equation of Straight Line
22. Normal Form of Equation of Straight Line
23. Problem1-Normal Form of Equation of Straight Line
24. How 2 Variabled Linear Equation Represent Straight Line
25. Problem1-How 2 Variabled Linear Equation Represent Straight Line
26. Transforming General Linear Equation to Standard Forms
27. Problem1-Transforming General Linear Equation to Standard Forms
28. Transforming General Equation to Slope Intercept Form
29. Problem1-Transforming General Equation to Slope Intercept Form
30. Transforming General Form of Equation to Intercept Form
31. Problem1-Transforming General Form of Equation to Intercept Form
32. Transforming General Form of Equation to Normal Form
33. Problem1-Transforming General Form of Equation to Normal Form
34. Transforming General Form of Equation to Point Slope Form
35. Problem1-Transforming General Form of Equation to Point Slope Form
36. Transforming General Form of Equation to Symmetric Form
37. Problem1-Transforming General Form of Equation to Symmetric Form
38. Position of Point with Respect to Line
39. More on Position of Point with Respect to Line
40. Problem1-Position of Point with Respect to Line

18.4: Two and Three Straight Lines

1. Relationship between Two and Three Straight Lines
2. The Point of Intersection of Straight Lines
3. Problem1-The Point of Intersection of Straight Lines
4. Condition of Concurrency of Three Straight Lines
5. More on Condition of Concurrency of Three Straight Lines
6. Problem1-Condition of Concurrency of Three Straight Lines
7. Equation of Lines Through Point of Intersecting 2 Lines
8. Problem1-Equation of Lines Through Point of Intersecting 2 Lines
9. Condition that Altitudes of Triangle are Concurrent
10. Moreo on Condition that Altitudes of Triangle are Concurrent
11. Problem1-Condition that Altitudes of Triangle are Concurrent
12. Condition that Right Bisectors of Triangle are Concurrent
13. More on Condition that Right Bisectors of Triangle Concurrent
14. Problem1-Condition that Right Bisectors of Triangle are Concurrent
15. Distance of Point From Line
16. Problem1-Distance of Point From Line
17. Distance between Two Parallel Lines
18. Problem1-Distance between Two Parallel Lines
19. Area of Triangular Region With Given Vertices
20. More on Area of Triangular Region With Given Vertices
21. Problem1-Area of Triangular Region With Given Vertices

18.5: Angles Between Two Lines

1. Angle Between Two Lines
2. Problem1-Angle Between Two Lines
3. Problem2-Angle Between Two Lines
4. Equation of a Straight Line in Matrix Form
5. More on Equation of Straight Line in Matrix Form
6. Problem1-Equation of a Straight Line in Matrix Form
7. Problem2-Equation of a Straight Line in Matrix Form

18.6: Homogeneous Equations-Second Degree in2 Variables

1. Homogeneous Equation of Second Degree in Two Variables
2. More on Homogeneous Equation of 2nd Degree in 2 Variables
3. Homogeneous Equation of Degree 'n'
4. More on Homogeneous Equation of Degree 'n'
5. Problem1-Homogeneous Equation of Degree 'n'
6. Problem2-Homogeneous Equation of Degree 'n'
7. Problem2-More on Homogeneous Equation of Degree 'n'
8. Problem3-Homogeneous Equation of Degree 'n'
9. Condition For the Lines to be Coincident
10. More on Condition For the Lines to be Coincident