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Working in Three Dimensions

Dive into the world of conic sections in geometry, from identifying circles, ellipses, hyperbolas, and parabolas to understanding their generation through cutting a cone. Explore equations, distances, and shapes in 2D and 3D.

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Working in Three Dimensions

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  1. Working in Three Dimensions

  2. Question 1 - 10 • Identify the four conics.

  3. Answer 1 – 10 • Circle, ellipse, hyperbola, parabola

  4. Question 1 - 20 • Provide a description of how conics are generated and what determines the particular shapes.

  5. Answer 1 – 20 • Conics are formed when a double napped cone is cut by a plane. The angle of the plane determines the type of conic formed.

  6. Question 1 - 30 • Find the distance between the points (2,-4) and (-1,-2)

  7. Answer 1 – 30

  8. Question 1 - 40 • Find the midpoint of the segment joining the points (2,-4) and (-1,-2)

  9. Answer 1 – 40 • (1/2,-3)

  10. Question 1 - 50 • Determine the type of triangle formed with vertices (5, 3), (7,-1)and (2,1). Choose from the possible answers of isosceles, equilateral and scalene.

  11. Answer 1 – 50

  12. Question 2 - 10 • Find the standard form of a parabola with vertex (0,0) and focus (0,1).

  13. Answer 2 – 10

  14. Question 2 - 20 • Find the standard equation of the parabola with focus (2,3) and directrix y = 7

  15. Answer 2 – 20

  16. Question 2 - 30 • Write the equation of the parabola shown below in standard conic form.

  17. Answer 2 – 30

  18. Question 2 - 40

  19. Answer 2 – 40

  20. Question 2 - 50 • Television Antenna Dish The cross section of a television antenna • dish is a parabola. For the dish at the right, the receiver is located at • the focus, 3.5 feet above the vertex. Find an equation for the cross • Section of the dish. (Assume the vertex is at the origin.)

  21. Answer 2 – 50

  22. Question 3 - 10 • Write the equation of a circle with center (2,1) and radius 9

  23. Answer 3 – 10

  24. Question 3 - 20 • Write the equation of the following circle in standard form.

  25. Answer 3 – 20

  26. Question 3 - 30 • Write the equation of a circle with diameter endpoints of (-2,4) and (6,4)

  27. Answer 3 – 30

  28. Question 3 - 40

  29. Answer 3 – 40

  30. Question 3 - 50

  31. Answer 3 – 50

  32. Question 4 - 10 • Write the general form of the equation of an ellipse and explain each piece of the formula.

  33. Answer 4 – 10

  34. Question 4 - 20 Write the equation of the following Ellipse:

  35. Answer 4 – 20

  36. Question 4 - 30 Write the equation of an ellipse with foci (0,2), (8,2) and a minor axis length of 2. Find the coordinates of the foci as well.

  37. Answer 4 – 30

  38. Question 4 - 40

  39. Answer 4 – 40

  40. Question 4 - 50 • In its orbit, Mercury ranges between 46.04 million kilometers and 69.86 million kilometers from the sun. Use this information and the diagram shown at the right to write an equation for the orbit of Mercury.

  41. Answer 4 – 50 • Solution

  42. Question 5 - 10

  43. Answer 5 – 10

  44. Question 5 - 20

  45. Answer 5 – 20

  46. Question 5 - 30

  47. Answer 5 – 30

  48. Question 5 - 40

  49. Answer 5 – 40

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