1 / 59

Chapter 12: Conic Sections

Chapter 12: Conic Sections. 12.1 Parabola (Distance Formula) (Midpoint Formula) Circle 12.2 Ellipse 12.3 Hyperbola 12.4 Nonlinear Systems. Sections of a Cone. circle. ellipse. parabola. Sections of a Cone ... continued. hyperbola.

bkarl
Download Presentation

Chapter 12: Conic Sections

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 12: Conic Sections • 12.1 Parabola (Distance Formula) (Midpoint Formula) Circle • 12.2 Ellipse • 12.3 Hyperbola • 12.4 Nonlinear Systems Math 120 - KM

  2. Sections of a Cone circle ellipse parabola KM & PP AIM2

  3. Sections of a Cone ... continued hyperbola KM & PP AIM2

  4. Degenerate Conic Sections point line Intersecting lines KM & PP AIM2

  5. 12.1 Parabolas and Circles Math 120 - KM

  6. The Parabola 12.1 Math 120 - KM

  7. Can You Hear a Pin Drop? A Parabolic Reflector For a Microphone 12.1 Math 120 - KM

  8. Architectural Parabola A Parabolic Archway 12.1 Math 120 - KM

  9. Shine Your Light Forward A Parabolic Headlight 12.1 Math 120 - KM

  10. Parabolic Shadows 12.1 Math 120 - KM

  11. 12.1 The Basic Ideas 12.1 Math 120 - KM

  12. 9.1 Ex 1: y = 2x2 + 8x + 5 Vertex: (-2, -3) Opens upwards (narrow) Axis of symmetry: x = -2 y -intercept: (0,5) 12.1 {-4,2} {5/3} {17.5327} {3} Math 120 - KM

  13. 9.1 Ex 1: y = 2x2 + 8x + 5alternate method Vertex: (-2, -3) Opens upwards (narrow) Axis of symmetry: x = -2 y -intercept: (0,5) 12.1 {-4,2} {5/3} {17.5327} {3} Math 120 - KM

  14. 9.1 Ex 2: y = -6x2 + 12x - 2 Vertex: (1, 4) Opens downward (narrow) Axis of symmetry: x = 1 y -intercept: (0,-2) 12.1 {-4,2} {5/3} {17.5327} {3} Math 120 - KM

  15. 9.1 Ex 2: y = -6x2 + 12x – 2alternate method Vertex: (1, 4) Opens downward (narrow) Axis of symmetry: x = 1 y -intercept: (0-2) 12.1 Math 120 - KM

  16. 12.1 Ex 3: x = 2y2 – 8y + 5 Vertex: (-3, 2) Opens to the right (narrow) Axis of symmetry: y = 2 x – intercept: (5, 0) 12.1 Math 120 - KM

  17. 12.1 Ex 3: x = 2y2 – 8y + 5alternate method Vertex: (-3, 2) Opens to the right (narrow) Axis of symmetry: y = 2 x – intercept: (5, 0) 9.1 Math 120 - KM

  18. 12.1 Ex 4: x = -2y2 – 4y - 3 Vertex: (-1, -1) Opens to the left (narrow) Axis of symmetry: y = -1 x – intercept: (-3, 0) 12.1 Math 120 - KM

  19. 12.1 Ex 4: x = -2y2 – 4y – 3alternate method Vertex: (-1, -1) Opens to the left (narrow) Axis of symmetry: y = -1 x – intercept: (-3, 0) 12.1 Math 120 - KM

  20. The Distance Formula y c b x a 12.1 Math 120 - KM

  21. 12.1 Distance Formula Examples Determine the distance from P1 to P2. P1 (-2, 3) P2(2, 0) P1 (5, -2) P2(-3, -1) 12.1 Math 120 - KM

  22. 9.1 MIDPOINT Find the point exactly halfway from (-3,0) to (0,4) (0, 4) M(-1.5, 2) (0, 0) (-3, 0) 9.1 Math 120 - KM

  23. y x 12.1 Average the Coordinates! AVERAGE ! 12.1 Math 120 - KM

  24. 12.1 Midpoint Examples Determine the midpoint ofP1P2. P1 (-2, 3) P2(2, 0) P1 (5, -2) P2(-3, -1) 12.1 Math 120 - KM

  25. 12.1 Circles With a COMPASS How do I make a circle? 12.1 krm 11.2

  26. 12.1 Circle: Center (h,k) Radius r (h,k) r The set of all points in a plane that are at a fixed distance, r, called the radius from a fixed point, (h, k), called the center. 12.1 krm 11.2

  27. 12.1 x2 + y2 = 1 Center: (0, 0) Radius: 1 The Unit Circle 12.1 Math 120 - KM

  28. 12.1 (x + 2)2 + (y – 4)2 = 32 Center: (-2, 4) Radius: 3 12.1 Math 120 - KM

  29. 12.1 x2 + (y + 4)2 = 25 Center: (0, - 4) Radius: 5 12.1 Math 120 - KM

  30. 12.1 Write the equation of the circle withradius 7 and center (-5, 8). 12.1 krm 11.2

  31. The Equation of a Circle How do I know it’s a circle? Look for ax2+ay2 12.1 krm 11.2

  32. Circle: Standard Form Write the equation of the circle in standard form and sketch the graph: x2 + y2 - 6x + 10y + 25 = 0 Center: (3, - 5) Radius: 3 9.1 krm 11.2

  33. 12.2 The Ellipse The Ellipse 12.2 Math 120 - KM

  34. 12.2 Ellipse (it fits in a box!) x-intercepts (+ a, 0) y-intercepts (0, + b) 12.2 Math 120 - KM

  35. 12.2 Example: Horizontal Major Axis 12.2 Math 120 - KM

  36. 12.2 Example: Vertical Major Axis 12.2 Math 120 - KM

  37. 12.2 Example: center not at the origin 12.2 Math 120 - KM

  38. 12.2 Example: Put in Standard Form First 12.2 Math 120 - KM

  39. 12.2 Example continued:Put in Standard Form First 12.2 Math 120 - KM

  40. 12.3 The Hyperbolait fits outside the box The Hyperbola X y 12.3 Math 120 - KM

  41. 12.3 The HyperbolaSTANDARD FORM X y 12.3 Math 120 - KM

  42. 12.3 Hyperbola: x2 is first • Fundamental Rectangle • Asymptotes • Vertices (if x2 – y2…) • Sketch X 12.3 Math 120 - KM

  43. 12.3 Example x2 is first 12.3 Math 120 - KM

  44. 12.3 Hyperbola: y2 is first • Fundamental Rectangle • Asymptotes • Vertices (if y2 – x2…) • Sketch y 12.3 Math 120 - KM

  45. 12.3 Example y2 is first y 12.3 Math 120 - KM

  46. 12.3 The HyperbolaNONSTANDARD FORM + + - - 12.3 Math 120 - KM

  47. 12.3 The HyperbolaNONSTANDARD FORMExample 1 12.3 Math 120 - KM

  48. 12.3 The HyperbolaNONSTANDARD FORMExample 2 12.3 Math 120 - KM

  49. Conics...2300+ years old? Math 120 - KM

  50. 12.4 Nonlinear Systems 12.4 Math 120 - KM

More Related