Chapter 6: Conic Section

6.1: Introduction

1. Introduction to Conic Section
2. More on Introduction to Conic Section
3. Standard Form of Equation of Circle
4. General Form of Equation of Circle
5. More on General Form of Equation of Circle
6. Equation of Circle Passing Though Three Non-Collinear Points
7. More on Equation of Circle Passsing Through 3 Non-Collinear Points
8. Equation of Circle Passing Through 2 Points and its Centre on Line
9. Equation-Circle Passing Though 2 Points with 1 Tangential Point
10. Equation-Circle Passing Though 2 Points with 1 Tangential Point-1
11. Equation-Circle Passing Through 2 Points and Line
12. Equation-Circle Passing Through 2 Points and Line

6.2: Tangents and Normals

1. Equation of Tangent to Circle
2. More on Equation of Tangent to Circle
3. Problem1- Equation of Tangent to Circle
4. Problem2a-Equation of Tangent to Circle
5. Problem2b-Equation of Tangent to Circle
6. Equation of Normal to Circle
7. Problem-Points Lie Inside, Outside or on the Circle
8. Points Lie Inside, Outside or on the Circle
9. More on Points Lie Inside, Outside or on the Circle
10. Line Intersects Circle at Most 2 Points
11. Condition that Line may be Tangent to Circle

6.3: Analytical Proofs of Important Properties of a Circle

1. Proof-2 Tangents can be Drawn to Circle from Point
2. More on Proof-2 Tangents can be Drawn to Circle from Point
3. Length of Tangent to Circle
4. To Prove Circles Diameter is 2 Times its Radius
5. Chords Perpendicular Passes Centre of Circle
6. More on Chords Perpendicular Passes Centre of Circle
7. Line From Centre and Midpoint of Chord is Perp to it
8. More on Line From Centre and Midpoint of Chord is Perp to it
9. Congruent Chords are Equidistance from Centre of Circle
10. More on Congruent Chords are Equidistance from Centre of Circle
11. Angle in Semi-Circle is Right Angle
12. More on Angle in Semi-Circle is Right Angle
13. Perpendicular Radial Segment is Tangent to Circle
14. More on Perpendicular Radial Segment is Tangent to Circle
15. Tangent to Circle is Perpendicular to Radial Segment

6.4: Parabola

1. Introduction to Parabola
2. More on Introduction to Parabola
3. Terms Related to Parabola
4. General Form of Equation of Parabola
5. Other Standard Parabola
6. Graph of Parabola Facing Upward
7. Graph of Parabola Facing Downward
8. Graph of Parabola Facing Rightward
9. Graph of Parabola Facing Leftward
10. Problem Related with Parabola
11. Parabola with Vertex not at Origin
12. More on Parabola with Vertex not at Origin
13. Problem-Parabola with Vertex not at Origin
14. Graphing Parabola with Vertex not at Origin
15. More on Graphing Parabola with Vertex not at Origin
16. Finding Equation of Parabola with Focus and Vertex
17. Finding Equation of Parabola with Directrix and Vertex
18. Problem1-Finding Equation of Parabola with Focus and Vertex
19. Problem2-Finding Equation of Parabola with Focus and Vertex
20. Problem3-Finding Equation of Parabola with Focus and Vertex

6.5: Ellipse and Its Elements

1. Obtaining Standard Equation of Ellipse
2. More on Obtaining Standard Equation of Ellipse-1
3. More on Obtaining Standard Equation of Ellipse-2
4. More on Obtaining Standard Equation of Ellipse-3
5. Circle as Special Case of Ellipse
6. Basic Terms Associated with Ellipse
7. More on Basic Terms Associated with Ellipse
8. Standard Form of Vertical and Horizontal Ellipses
9. Problem1-Standard Form of Vertical and Horizontal Ellipses
10. Translation of Horizontal Ellipse
11. More on Translation of Horizontal Ellipse
12. Translation of Vertical Ellipse
13. More on Translation of Vertical Ellipse
14. Equation of Ellipse with Foci and Vertices
15. Problem1-Equation of Ellipse with Foci and Vertices
16. Problem3-Equation of Ellipse with Foci and Vertices
17. Ellipse Equation with Centre and Length of Axes
18. Ellipse Equation with Centre and Given Point
19. More on Ellipse Equation with Centre and Given Point
20. Ellipse Equation with Vertices and Eccentricity
21. Ellipse Equation with Vertices & Length of Semi-minor Axis

6.6: Hyperbola and Its Elements

1. Defining Hyperbola
2. Standard Form of Equation of Hyperbola
3. More on Standard Form of Equation of Hyperbola
4. More on Standard Form of Equation of Hyperbola
5. Asymptotes of Hyperbola
6. Foci of Hyperbola
7. More on Foci of Hyperbola
8. Problem1-Foci of Hyperbola
9. Horizontal Hyperbola
10. Vertical Hyperbola
11. Rectangular Hyperbola
12. Graphing Hyperbola
13. More on Graphing Hyperbola
14. Problem1-Graphing Hyperbola
15. Problem2-Graphing Hyperbola
16. Hyperbola with Focus and Eccentricity
17. Graphing Hyperbola with Eccentricity and Latus Rectum
18. Graphing Hyperbola with Focus and Directrix
19. Translation of Hyperbola with Horizontally
20. More on Translation of Hyperbola with Horizontally
21. Translation of Hyperbola Vertically
22. More on Translation of Vertical Hyperbola

6.7: Tangents and Normals

1. Intersection of Line and Parabola
2. More on Intersection of Line and Parabola
3. Equation of Tangent Line to Parabola in Slope Form
4. Equation of Tangent Line to Parabola at Given Point
5. More on Equation of Tangent Line to Parabola at Given Point
6. Problem-Equation of Tangent Line to Parabola at Given Point
7. Equation of Normal Line to Parabola at Given Point
8. Problem1-Equation of Normal Line to Parabola at Given Point
9. Application of Parabola-Suspension Related Problem
10. Reflecting Property of Parabola
11. Use of Parabola on Everyday Life-Problem
12. Points of Intersection of Line and Ellipse
13. More on Points of Intersection of Line and Ellipse
14. Condition of Tangency of Line to Ellipse
15. Equation of Tangent to Ellipse at Point
16. More on Equation of Tangent to Ellipse at Point
17. Equation of Normal to Ellipse at Point
18. More on Equation of Normal to Ellipse at Point
19. Problem1a-Equation of Normal to Ellipse at Point
20. Problem1b-Equation of Normal to Ellipse at Point
21. Graph of Ellipse
22. More on Graph of Ellipse
23. Point of Intersection of Line with Hyperbola
24. Condition of Tangency of Line to Hyperbola
25. Problem- Condition of Tangency of Line to Hyperbola
26. Equation of Tangent Line to Hyperbola at Point
27. More on Equation of Tangent Line to Hyperbola at Point
28. Problem- Equation of Tangent Line to Hyperbola at Point
29. Equation of Normal Line to Hyperbola at Point
30. More on Equation of Normal Line to Hyperbola at Point
31. Intersection of Two Conics
32. More on Intersection of Two Conics
33. Problem1a-Intersection of Two Conics
34. Problem1b-Intersection of Two Conics

6.8: 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 axis
6. More on Rotation of Axes
7. Rotation of Conic
8. More on Rotation of Conic
9. Problem1a-Rotation of Conic
10. Problem1b-Rotation of Conic
11. Problem1b-Rotation of Conic
12. Problem1d-Rotation of Conic
13. Problem2a-Rotation of Conic
14. Problem2b-Rotation of Conic

6.9: The General Equation of Second Degree

1. General Degree of 2nd Degree Equation-Circle
2. General Degree of 2nd Degree Equation-Ellipse
3. General Degree of 2nd Degree Equation-Hyperbola
4. General Degree of 2nd Degree Equation-Parabola
5. Classification of Conic by Discriminant
6. Finding Angle of Rotation in Conic
7. More on Finding Angle of Rotation in Conic
8. Further stuff on Finding Angle of Rotation in Conic
9. Problem1-Finding Angle of Rotation in Conic