MODULE 1 - PRE CALCULUS STEM 11 CONIC SECTIONS
- 1. PRE-CALCULUS QUARTER 1 – MODULE 1: CONIC SECTIONS
- 2. What I need to know In the end of the module the learner shall be able to: Illustrate the different types of conic sections: parabola, ellipse, circle, hyperbola, and the degenerate cases. (STEM_PC11AG – ia – 1) a. Describe the type of conic sections formed when the conic is cut; b. Illustrate the types of conic sections; and c. Name examples of conic sections used in the real world.
- 3. “GOOD AND EVIL HAVE AN EQUAL SHARE IN MOLDING CHARACTER, AND IN SOME INSTANCES, MISERY IS A GREATER TEACHER THAN HAPPINESS.” HOW IS IT RELATED IN FORMING DIFFERENT CONIC SECTIONS?
- 4. What I know CHOOSE THE LETTER OF THE CORRECT ANSWER. 1. What is a solid figure whose base is a circle and joined by a point, called the vertex, to the curve part? a. Cylinder c. Cone b. Pyramid d. Prism
- 5. What I know CHOOSE THE LETTER OF THE CORRECT ANSWER. 2. Which of the following is formed when the plane is cut and parallel to one and only one generator of the cone? a. Circle c. Ellipse b. Parabola d. Hyperbola
- 6. What I know CHOOSE THE LETTER OF THE CORRECT ANSWER. 3. Which of the following is formed when a plane and a double right circular cone intersect? a. Circle c. Conic b. Generator of the cone d. Nappe
- 7. What I know CHOOSE THE LETTER OF THE CORRECT ANSWER. 4. Which of the following is formed when a plane and a double right circular cone intersect but not a curve? a. conic section c. generator of a cone b. degenerated conic d. nappes
- 8. What I know CHOOSE THE LETTER OF THE CORRECT ANSWER. 5. Which of the following is formed when the plane is cut, and it is parallel to two generators of the cone. a. circle c. ellipse b. parabola d. hyperbola
- 9. What I know CHOOSE THE LETTER OF THE CORRECT ANSWER. 6. Which of the following is formed when the plane is cut and is not parallel to any generator of the cone? a. Circle c. Ellipse b. Parabola d. Hyperbola
- 10. What I know CHOOSE THE LETTER OF THE CORRECT ANSWER. 7. Which of the following is formed when the plane is cut and not parallel to any generator but perpendicular to the axis? a. Circle c. Ellipse b. Parabola d. Hyperbola
- 11. What I know CHOOSE THE LETTER OF THE CORRECT ANSWER. 8. What is the fixed point of the conic? a. Vertex c. Nappe b. Generator of the cone d. Axis
- 12. What I know CHOOSE THE LETTER OF THE CORRECT ANSWER. 9. What is a line lying entirely on the cone? a. Generator of the cone c. Nappe b. Vertex d. Axis
- 13. What I know CHOOSE THE LETTER OF THE CORRECT ANSWER. 10. What is the point of intersection of the conics? a. Vertex c. Generator of the cone b. Nappe d. Axis
- 14. What I know CHOOSE THE LETTER OF THE CORRECT ANSWER. 11. Which of the following conic has the eccentricity of 1?(e=1) a. Circle c. Ellipse b. Parabola d. Hyperbola
- 15. What I know CHOOSE THE LETTER OF THE CORRECT ANSWER. 12. Which of the following objects can be classified as a circle? a. planet earth c. basin b. orbit of the planet d. ring
- 16. What I know CHOOSE THE LETTER OF THE CORRECT ANSWER. 13. Which of the following is not formed when there is a degenerate conic section? a. Point c. Plane b. Line d. Solid figure
- 17. What I know CHOOSE THE LETTER OF THE CORRECT ANSWER. 14. Which of the two figure formed an ellipse? a. Figure 1 b. Figure 2 c. Figure 1 and 2 d. None of these
- 18. What I know CHOOSE THE LETTER OF THE CORRECT ANSWER. 15. Which of the following figure illustrate a degenerate conic section? a. Figure 1 b. Figure 2 c. Figure 1 and 2 d. None of these
- 19. Conic sections Appollonius of perga, the “great geometer “studied the curves formed by intersection of a plane and a double right circular cone and discovered many of its properties. Conic sections are obtained by the intersection of plane and a cone. Appollonius of perga,
- 20. What’s in Identify the geometric figure or term being represented by the following objects. CIRCLE ELLIPSE POINT
- 21. What’s in Identify the geometric figure or term being represented by the following objects. PARABOLA HYPERBOLA LINE
- 22. What’s in Identify the geometric figure or term being represented by the following objects. ELLIPSE CIRCLE PARABOLA
- 23. What’s in Identify the geometric figure or term being represented by the following objects. PLANE HYPERBOLA CIRCLE
- 24. What’s in Identify the geometric figure or term being represented by the following objects. HYPERBOLA PARABOLA CIRCLE
- 25. What’s New Arrange the jumbled words to find the correct answer that satisfy the following statement. 1. If the cutting plane is not parallel to one and only one generator. B o R a p a l a paRaBola
- 26. What’s New Arrange the jumbled words to find the correct answer that satisfy the following statement. 2. If the cutting plane is not parallel to any generator. P e L i e s L eLLipse
- 27. What’s New Arrange the jumbled words to find the correct answer that satisfy the following statement. 3. If the cutting plane is parallel to two generators. P y H e b r o a l HyPerbola
- 28. What’s New Arrange the jumbled words to find the correct answer that satisfy the following statement. 4. If the cutting plane is not parallel to any generator but perpendicular to the axis. R i C C e l CiRCle
- 29. What’s New Arrange the jumbled words to find the correct answer that satisfy the following statement. 5. The fixed point of the conics. X E r e T v verTEX
- 30. H W R T E M A D E Q S V G Y R A T E N A L P C N E D P A R A B O L A I O F A O E E Z C V I R R I U J E V R U C C P P C S L I N E Z B B D S O L E W D T X Z C O N E I E R C O V I D Q B L A N M S K X E T R E V J A T T I What’s New Find the word/ set of words on the puzzle. In what row or column?
- 31. What is It Conic Sections
- 32. What is It A conic section is a curved formed by the intersection of the plane. The three types of conics: parabola, hyperbola, ellipse and the circle a special type of conics. Conic sections are formed when a plane intersects a cone. A cone has two identical parts called the nappes. Conic Sections
- 34. A circle is formed when the plane is perpendicular to the axis.
- 35. A parabola is formed when the plane is parallel to the generating line.
- 36. An ellipse is formed when the plane intersects one nappe of the cone at an angle to the axis.
- 37. A hyperbola if formed when the plane intersects both halves of a double cone but not passing through the axis.
- 38. The degenerated conic sections are not curves but formed by the intersection of the plane and a double right circular cone. 1. Point 2. Line 3. Intersecting lines
- 39. There are other ways for a plane and the cones to intersect, to form what are referred to as degenerate conics: a point, one line, and two lines. See Figures 1.4, 1.5 and 1.6.
- 40. A degenerate conic is generated when a plane intersects the vertex of the cone. There are three types of degenerate conics: 1. The degenerate form of a circle or an ellipse is a singular point. 2. The degenerate form of a parabola is a line or two parallel lines. 3. The degenerate form of a hyperbola is two intersecting lines.
- 41. ECCENTRICITY The eccentricity e of a conic section is defined to the distance from any point on the conic section to its focus, divided by the perpendicular distance from that point to the nearest directrix. e = 1 0 < e < 1 e > 1 e = 0
- 42. 0 < e < 1 e > 1 e = 1
- 43. What I Have Learned I. Draw the indicated curve on the cone using a plane. 1. Circle 3. Ellipse 2. Hyperbola 4. Parabola
- 44. II. Identify whether the following objects represent ellipse, hyperbola, circle, or parabola. 1. Banana 6. Satellite dish 2. Basketball ring 7. Tire 3. Eiffel tower 8. Mcdonald’s logo 4. Orbit of the planet 9. Tornado 5. Rainbow 10. Hourglass 11. Rugby ball parabola circle hyperbola ellipse parabola parabola circle parabola hyperbola hyperbola ellipse
- 45. What Can I Do Triple Pairing A. Match column A to column B. And then match column B to column C.
- 46. What Can I Do B. Create at least five of an illustrations that you can find at your home and satisfied the four types of conic section.
- 47. Assessment Choose the letter of the correct answer. 1. The curve formed when the intersection of a plane and a double right circular cone. a. Circle c. conic b. Generator of the cone d. nappe
- 48. Assessment Choose the letter of the correct answer. 2. A solid figure whose base is a circle and joined by a point, called the vertex, to the curve part. a. Cylinder c. Cone b. Pyramid d. Prism
- 49. Assessment Choose the letter of the correct answer. 3. When the plane is cut and parallel to one and only one generator of the cone. a. Circle c. Ellipse b. Parabola d. Hyperbola
- 50. Assessment Choose the letter of the correct answer. 4. The curve form when the plane cuts the two generators of the cone. a. Circle c. Ellipse b. Parabola d. Hyperbola
- 51. Assessment Choose the letter of the correct answer. 5. The intersection of the plane and a double right circular cone but not a curve. a. Conic section c. generator of a cone b. degenerated conic d. nappes
- 52. Assessment Choose the letter of the correct answer. 6. The fixed point of the conic. a. Vertex c. Nappe b. Generator of the cone d. Axis
- 53. Assessment Choose the letter of the correct answer. 7. If the eccentricity of the conic is e = 1. a. Circle c. Ellipse b. Parabola d. Hyperbola
- 54. Assessment Choose the letter of the correct answer. 8. Curve when the plane is cut and not parallel to any generator but perpendicular to the axis. a. Circle c. Ellipse b. Parabola d. Hyperbola
- 55. Assessment Choose the letter of the correct answer. 9. The curved form when the plane is cut and is not parallel to any generator of the cone. a. Circle c. Ellipse b. Parabola d. Hyperbola
- 56. Assessment Choose the letter of the correct answer. 10. A line lying entirely on the cone. a. Generator of the cone c. Nappe b. Vertex d. Axis
- 57. Assessment Choose the letter of the correct answer. 11. The point of intersection of the conics. a. Vertex c. Generator of the cone b. Nappe d. Axis
- 58. Assessment Choose the letter of the correct answer. 12. Which of the following objects cannot be classified as a circle? a. planet earth c. basin b. orbit of the planet d. ring
- 59. Assessment Choose the letter of the correct answer. 13. The following is formed when there is a degenerate conic section EXCEPT: a. Point c. Plane b. Line d. Intersecting lines
- 60. Assessment Choose the letter of the correct answer. 14. Which of the two figure formed an hyperbola? a. Figure 1 c. Figure 1 and 2 b. Figure 2 d. None of these
- 61. Assessment Choose the letter of the correct answer. 15. The figure which illustrate a degenerate conic section is _________. a. Figure 1 c. Figure 1 and 2 b. Figure 2 d. None of these
- 62. Assessment Choose the letter of the correct answer. 1. The curve formed when the intersection of a plane and a double right circular cone. a. Circle c. conic b. Generator of the cone d. nappe
- 63. Assessment Choose the letter of the correct answer. 2. A solid figure whose base is a circle and joined by a point, called the vertex, to the curve part. a. Cylinder c. Cone b. Pyramid d. Prism
- 64. Assessment Choose the letter of the correct answer. 3. When the plane is cut and parallel to one and only one generator of the cone. a. Circle c. Ellipse b. Parabola d. Hyperbola
- 65. Assessment Choose the letter of the correct answer. 4. The curve form when the plane cuts the two generators of the cone. a. Circle c. Ellipse b. Parabola d. Hyperbola
- 66. Assessment Choose the letter of the correct answer. 5. The intersection of the plane and a double right circular cone but not a curve. a. Conic section c. generator of a cone b. degenerated conic d. nappes
- 67. Assessment Choose the letter of the correct answer. 6. The fixed point of the conic. a. Vertex c. Nappe b. Generator of the cone d. Axis
- 68. Assessment Choose the letter of the correct answer. 7. If the eccentricity of the conic is e = 1. a. Circle c. Ellipse b. Parabola d. Hyperbola
- 69. Assessment Choose the letter of the correct answer. 8. Curve when the plane is cut and not parallel to any generator but perpendicular to the axis. a. Circle c. Ellipse b. Parabola d. Hyperbola
- 70. Assessment Choose the letter of the correct answer. 9. The curved form when the plane is cut and is not parallel to any generator of the cone. a. Circle c. Ellipse b. Parabola d. Hyperbola
- 71. Assessment Choose the letter of the correct answer. 10. A line lying entirely on the cone. a. Generator of the cone c. Nappe b. Vertex d. Axis
- 72. Assessment Choose the letter of the correct answer. 11. The point of intersection of the conics. a. Vertex c. Generator of the cone b. Nappe d. Axis
- 73. Assessment Choose the letter of the correct answer. 12. Which of the following objects cannot be classified as a circle? a. planet earth c. basin b. orbit of the planet d. ring
- 74. Assessment Choose the letter of the correct answer. 13. The following is formed when there is a degenerate conic section EXCEPT: a. Point c. Plane b. Line d. Intersecting lines
- 75. Assessment Choose the letter of the correct answer. 14. Which of the two figure formed an hyperbola? a. Figure 1 c. Figure 1 and 2 b. Figure 2 d. None of these
- 76. Assessment Choose the letter of the correct answer. 15. The figure which illustrate a degenerate conic section is _________. a. Figure 1 c. Figure 1 and 2 b. Figure 2 d. None of these
- 77. Additional Activities Lists types of conics section that you can find around you. Circle Ellipse Hyperbola Parabola
- 78. ACTIVITY Answer the following questions: 1. What is conic sections? 2. Give the 4 types of conic sections. 3. How the degenerate conics formed? 4. Give at least 3 examples of every conics.