11X1 T12 03 parametric coordinates (2011)

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1. Parametric Coordinates 2. Parametric CoordinatesCartesian Coordinates: curve is described by one equation and points are described by two numbers. 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 pointsare described by one number (parameter). 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 pointsare described by one number (parameter).y x 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 pointsare described by one number (parameter).y x 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 pointsare described by one number (parameter).yx 2 4ay x 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 pointsare described by one number (parameter).yx 2 4ayCartesian equation x 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 pointsare described by one number (parameter).yx 2 4ay Cartesian equationx 2at , y at 2 x 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 pointsare described by one number (parameter).yx 2 4ay Cartesian equationx 2at , y at 2Parametric coordinates x 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 pointsare described by one number (parameter).y x 2 4ay Cartesian equation x 2at , y at 2Parametric coordinates (2a, a) x 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 pointsare described by one number (parameter).y x 2 4ay Cartesian equation x 2at , y at 2Parametric coordinates (2a, a)Cartesian coordinates x 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 pointsare described by one number (parameter).y x 2 4ay Cartesian equation x 2at , y at 2Parametric coordinates (2a, a)Cartesian coordinates t 1 x 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 pointsare described by one number (parameter).y x 2 4ay Cartesian equation x 2at , y at 2Parametric coordinates (2a, a)Cartesian coordinates t 1 parameter x 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 pointsare described by one number (parameter). yx 2 4ay Cartesian equation (4a, 4a) x 2at , y at 2Parametric coordinatest 2 (2a, a)Cartesian coordinates t 1 parameter x 15. Any point on the parabola x 2 4ay has coordinates; 16. Any point on the parabola x 2 4ay has coordinates;x 2at 17. Any point on the parabola x 2 4ay has coordinates;x 2at y at 2 18. Any point on the parabola x 2 4ay has coordinates;x 2at y at 2 where; a is the focal length 19. Any point on the parabola x 2 4ay has coordinates;x 2at y at 2 where; a is the focal lengtht is any real number 20. Any point on the parabola x 2 4ay has coordinates;x 2aty at 2where; a is the focal length t is any real numbere.g. Eliminate the parameter to find the cartesian equation of; 1 1x t , y t2 2 4 21. Any point on the parabola x 2 4ay has coordinates;x 2aty at 2where; a is the focal length t is any real numbere.g. Eliminate the parameter to find the cartesian equation of; 1 1x t , y t2 2 4 t 2x 22. Any point on the parabola x 2 4ay has coordinates;x 2aty at 2where; a is the focal length t is any real numbere.g. Eliminate the parameter to find the cartesian equation of;11x t , y t2241y 2x 2t 2x4 23. Any point on the parabola x 2 4ay has coordinates;x 2aty at 2where; a is the focal length t is any real numbere.g. Eliminate the parameter to find the cartesian equation of;11x t , y t224 1y 2x 2t 2x 4 y 4x2 1 4 y x2 24. Any point on the parabola x 2 4ay has coordinates;x 2at y at 2where; a is the focal length t is any real number e.g. Eliminate the parameter to find the cartesian equation of;1 1x t , y t22 4 1y 2x2 t 2x 4 y 4x2 1 4 y x2(ii) State the coordinates of the focus 25. Any point on the parabola x 2 4ay has coordinates;x 2at y at 2where; a is the focal length t is any real number e.g. Eliminate the parameter to find the cartesian equation of;1 1x t , y t22 4 1y 2x2 t 2x 4 y 4x2 1 4 y x2(ii) State the coordinates of the focus 1 a 4 26. Any point on the parabola x 2 4ay has coordinates;x 2at y at 2where; a is the focal length t is any real number e.g. Eliminate the parameter to find the cartesian equation of;1 1x t , y t22 4 1y 2x2 t 2x 4 y 4x2 1 4 y x2(ii) State the coordinates of the focus 1 a 1 focus 0, 4 4 27. (iii) Calculate the parametric coordinates of the curve y 8 x 2 28. (iii) Calculate the parametric coordinates of the curve y 8 x 2 x 2 4ay 29. (iii) Calculate the parametric coordinates of the curve y 8 x 2 x 2 4ay 1 4a 81a 32 30. (iii) Calculate the parametric coordinates of the curve y 8 x 2 x 2 4ay 1 4a 81a 32 1 1 the parametric coordinates are t , t 2 16 32 31. (iii) Calculate the parametric coordinates of the curve y 8 x 2 x 2 4ay 1 4a 81a 32 1 1 the parametric coordinates are t , t 2 16 32 Exercise 9D; 1, 2 (not latus rectum), 3, 5, 7a