11 x1 t11 03 parametric coordinates (2012)

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11 x1 t11 03 parametric coordinates (2012)

  1. 1. Parametric Coordinates
  2. 2. Parametric CoordinatesCartesian Coordinates: curve is described by one equation and points are described by two numbers.
  3. 3. Parametric CoordinatesCartesian Coordinates: curve is described by one equation and points are described by two numbers.Parametric Coordinates: curve is described by two equations and points are described by one number (parameter).
  4. 4. Parametric CoordinatesCartesian Coordinates: curve is described by one equation and points are described by two numbers.Parametric Coordinates: curve is described by two equations and points are described by one number (parameter). y x
  5. 5. Parametric CoordinatesCartesian Coordinates: curve is described by one equation and points are described by two numbers.Parametric Coordinates: curve is described by two equations and points are described by one number (parameter). y x
  6. 6. Parametric CoordinatesCartesian Coordinates: curve is described by one equation and points are described by two numbers.Parametric Coordinates: curve is described by two equations and points are described by one number (parameter). y x 2  4ay x
  7. 7. Parametric CoordinatesCartesian Coordinates: curve is described by one equation and points are described by two numbers.Parametric Coordinates: curve is described by two equations and points are described by one number (parameter). y x 2  4ay Cartesian equation x
  8. 8. Parametric CoordinatesCartesian Coordinates: curve is described by one equation and points are described by two numbers.Parametric Coordinates: curve is described by two equations and points are described by one number (parameter). y x 2  4ay Cartesian equation x  2at , y  at 2 x
  9. 9. Parametric CoordinatesCartesian Coordinates: curve is described by one equation and points are described by two numbers.Parametric Coordinates: curve is described by two equations and points are described by one number (parameter). y x 2  4ay Cartesian equation x  2at , y  at 2 Parametric coordinates x
  10. 10. Parametric CoordinatesCartesian Coordinates: curve is described by one equation and points are described by two numbers.Parametric Coordinates: curve is described by two equations and points are described by one number (parameter). y x 2  4ay Cartesian equation x  2at , y  at 2 Parametric coordinates (2a, a) x
  11. 11. Parametric CoordinatesCartesian Coordinates: curve is described by one equation and points are described by two numbers.Parametric Coordinates: curve is described by two equations and points are described by one number (parameter). y x 2  4ay Cartesian equation x  2at , y  at 2 Parametric coordinates (2a, a) Cartesian coordinates x
  12. 12. Parametric CoordinatesCartesian Coordinates: curve is described by one equation and points are described by two numbers.Parametric Coordinates: curve is described by two equations and points are described by one number (parameter). y x 2  4ay Cartesian equation x  2at , y  at 2 Parametric coordinates (2a, a) Cartesian coordinates t 1 x
  13. 13. Parametric CoordinatesCartesian Coordinates: curve is described by one equation and points are described by two numbers.Parametric Coordinates: curve is described by two equations and points are described by one number (parameter). y x 2  4ay Cartesian equation x  2at , y  at 2 Parametric coordinates (2a, a) Cartesian coordinates t 1 parameter x
  14. 14. Parametric CoordinatesCartesian Coordinates: curve is described by one equation and points are described by two numbers.Parametric Coordinates: curve is described by two equations and points are described by one number (parameter). y x 2  4ay Cartesian equation (4a, 4a) x  2at , y  at 2 Parametric coordinates t  2 (2a, a) Cartesian coordinates t 1 parameter x
  15. 15. Any point on the parabola x 2  4ay has coordinates;
  16. 16. Any point on the parabola x 2  4ay has coordinates; x  2at
  17. 17. Any point on the parabola x 2  4ay has coordinates; x  2at y  at 2
  18. 18. Any point on the parabola x 2  4ay has coordinates; x  2at y  at 2 where; a is the focal length
  19. 19. Any point on the parabola x 2  4ay has coordinates; x  2at y  at 2 where; a is the focal length t is any real number
  20. 20. Any point on the parabola x 2  4ay has coordinates; x  2at y  at 2 where; a is the focal length t is any real numbere.g. Eliminate the parameter to find the cartesian equation of; 1 1 x  t , y  t2 2 4
  21. 21. Any point on the parabola x 2  4ay has coordinates; x  2at y  at 2 where; a is the focal length t is any real numbere.g. Eliminate the parameter to find the cartesian equation of; 1 1 x  t , y  t2 2 4 t  2x
  22. 22. Any point on the parabola x 2  4ay has coordinates; x  2at y  at 2 where; a is the focal length t is any real numbere.g. Eliminate the parameter to find the cartesian equation of; 1 1 x  t , y  t2 2 4 1 y   2x 2 t  2x 4
  23. 23. Any point on the parabola x 2  4ay has coordinates; x  2at y  at 2 where; a is the focal length t is any real numbere.g. Eliminate the parameter to find the cartesian equation of; 1 1 x  t , y  t2 2 4 1 y   2x 2 t  2x 4 y   4x2  1 4 y  x2
  24. 24. Any point on the parabola x 2  4ay has coordinates; x  2at y  at 2 where; a is the focal length t is any real number e.g. Eliminate the parameter to find the cartesian equation of; 1 1 x  t , y  t2 2 4 1 y   2x 2 t  2x 4 y   4x2  1 4 y  x2(ii) State the coordinates of the focus
  25. 25. Any point on the parabola x 2  4ay has coordinates; x  2at y  at 2 where; a is the focal length t is any real number e.g. Eliminate the parameter to find the cartesian equation of; 1 1 x  t , y  t2 2 4 1 y   2x 2 t  2x 4 y   4x2  1 4 y  x2(ii) State the coordinates of the focus 1 a 4
  26. 26. Any point on the parabola x 2  4ay has coordinates; x  2at y  at 2 where; a is the focal length t is any real number e.g. Eliminate the parameter to find the cartesian equation of; 1 1 x  t , y  t2 2 4 1 y   2x 2 t  2x 4 y   4x2  1 4 y  x2(ii) State the coordinates of the focus  1 a 1  focus   0,  4  4
  27. 27. (iii) Calculate the parametric coordinates of the curve y  8 x 2
  28. 28. (iii) Calculate the parametric coordinates of the curve y  8 x 2 x 2  4ay
  29. 29. (iii) Calculate the parametric coordinates of the curve y  8 x 2 x 2  4ay 1 4a  8 1 a 32
  30. 30. (iii) Calculate the parametric coordinates of the curve y  8 x 2 x 2  4ay 1 4a  8 1 a 32 1 1   the parametric coordinates are  t , t 2   16 32 
  31. 31. (iii) Calculate the parametric coordinates of the curve y  8 x 2 x 2  4ay 1 4a  8 1 a 32 1 1   the parametric coordinates are  t , t 2   16 32  Exercise 9D; 1, 2 (not latus rectum), 3, 5, 7a
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