11X1 T11 03 parametric coordinates (2010)

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<ul><li><p>Parametric Coordinates </p></li><li><p>Parametric Coordinates Cartesian Coordinates: curve is described by one equation and points </p><p>are described by two numbers. </p></li><li><p>Parametric Coordinates Cartesian Coordinates: curve is described by one equation and points </p><p>are described by two numbers. </p><p>Parametric Coordinates: curve is described by two equations and points </p><p>are described by one number (parameter). </p></li><li><p>Parametric Coordinates Cartesian Coordinates: curve is described by one equation and points </p><p>are described by two numbers. </p><p>Parametric Coordinates: curve is described by two equations and points </p><p>are described by one number (parameter). </p><p>y </p><p>x </p></li><li><p>Parametric Coordinates Cartesian Coordinates: curve is described by one equation and points </p><p>are described by two numbers. </p><p>Parametric Coordinates: curve is described by two equations and points </p><p>are described by one number (parameter). </p><p>y </p><p>x </p></li><li><p>Parametric Coordinates Cartesian Coordinates: curve is described by one equation and points </p><p>are described by two numbers. </p><p>Parametric Coordinates: curve is described by two equations and points </p><p>are described by one number (parameter). </p><p>y </p><p>x </p><p>2 4x ay</p></li><li><p>Parametric Coordinates Cartesian Coordinates: curve is described by one equation and points </p><p>are described by two numbers. </p><p>Parametric Coordinates: curve is described by two equations and points </p><p>are described by one number (parameter). </p><p>y </p><p>x </p><p>2 4x ay Cartesian equation </p></li><li><p>Parametric Coordinates Cartesian Coordinates: curve is described by one equation and points </p><p>are described by two numbers. </p><p>Parametric Coordinates: curve is described by two equations and points </p><p>are described by one number (parameter). </p><p>y </p><p>x </p><p>2 4x ay Cartesian equation 22 , x at y at </p></li><li><p>Parametric Coordinates Cartesian Coordinates: curve is described by one equation and points </p><p>are described by two numbers. </p><p>Parametric Coordinates: curve is described by two equations and points </p><p>are described by one number (parameter). </p><p>y </p><p>x </p><p>2 4x ay Cartesian equation 22 , x at y at Parametric coordinates </p></li><li><p>Parametric Coordinates Cartesian Coordinates: curve is described by one equation and points </p><p>are described by two numbers. </p><p>Parametric Coordinates: curve is described by two equations and points </p><p>are described by one number (parameter). </p><p>y </p><p>x </p><p>2 4x ay Cartesian equation 22 , x at y at Parametric coordinates </p><p>(2 , )a a</p></li><li><p>Parametric Coordinates Cartesian Coordinates: curve is described by one equation and points </p><p>are described by two numbers. </p><p>Parametric Coordinates: curve is described by two equations and points </p><p>are described by one number (parameter). </p><p>y </p><p>x </p><p>2 4x ay Cartesian equation 22 , x at y at Parametric coordinates </p><p>(2 , )a a Cartesian coordinates </p></li><li><p>Parametric Coordinates Cartesian Coordinates: curve is described by one equation and points </p><p>are described by two numbers. </p><p>Parametric Coordinates: curve is described by two equations and points </p><p>are described by one number (parameter). </p><p>y </p><p>x </p><p>2 4x ay Cartesian equation 22 , x at y at Parametric coordinates </p><p>(2 , )a a Cartesian coordinates 1t </p></li><li><p>Parametric Coordinates Cartesian Coordinates: curve is described by one equation and points </p><p>are described by two numbers. </p><p>Parametric Coordinates: curve is described by two equations and points </p><p>are described by one number (parameter). </p><p>y </p><p>x </p><p>2 4x ay Cartesian equation 22 , x at y at Parametric coordinates </p><p>(2 , )a a Cartesian coordinates 1t parameter </p></li><li><p>Parametric Coordinates Cartesian Coordinates: curve is described by one equation and points </p><p>are described by two numbers. </p><p>Parametric Coordinates: curve is described by two equations and points </p><p>are described by one number (parameter). </p><p>y </p><p>x </p><p>2 4x ay Cartesian equation 22 , x at y at Parametric coordinates </p><p>(2 , )a a Cartesian coordinates 1t parameter </p><p>( 4 ,4 )a a2t </p></li><li><p>2 4x ayAny point on the parabola has coordinates; </p></li><li><p>2 4x ay</p><p>2x at</p><p>Any point on the parabola has coordinates; </p></li><li><p>2 4x ay</p><p>2x at2y at</p><p>Any point on the parabola has coordinates; </p></li><li><p>2 4x ay</p><p>2x at2y at</p><p>Any point on the parabola has coordinates; </p><p>where; a is the focal length </p></li><li><p>2 4x ay</p><p>2x at2y at</p><p>Any point on the parabola has coordinates; </p><p>where; a is the focal length </p><p>t is any real number </p></li><li><p>2 4x ay</p><p>2x at2y at</p><p>Any point on the parabola has coordinates; </p><p>where; a is the focal length </p><p>t is any real number </p><p>e.g. Eliminate the parameter to find the cartesian equation of; </p><p>21 1 , 2 4</p><p>x t y t </p></li><li><p>2 4x ay</p><p>2x at2y at</p><p>Any point on the parabola has coordinates; </p><p>where; a is the focal length </p><p>t is any real number </p><p>e.g. Eliminate the parameter to find the cartesian equation of; </p><p>21 1 , 2 4</p><p>x t y t </p><p>2t x</p></li><li><p>2 4x ay</p><p>2x at2y at</p><p>Any point on the parabola has coordinates; </p><p>where; a is the focal length </p><p>t is any real number </p><p>e.g. Eliminate the parameter to find the cartesian equation of; </p><p>21 1 , 2 4</p><p>x t y t </p><p>2t x 21</p><p>24</p><p>y x</p></li><li><p>2 4x ay</p><p>2x at2y at</p><p>Any point on the parabola has coordinates; </p><p>where; a is the focal length </p><p>t is any real number </p><p>e.g. Eliminate the parameter to find the cartesian equation of; </p><p>21 1 , 2 4</p><p>x t y t </p><p>2t x 21</p><p>24</p><p>y x</p><p> 2</p><p>2</p><p>14</p><p>4y x</p><p>y x</p></li><li><p>2 4x ay</p><p>2x at2y at</p><p>Any point on the parabola has coordinates; </p><p>where; a is the focal length </p><p>t is any real number </p><p>e.g. Eliminate the parameter to find the cartesian equation of; </p><p>21 1 , 2 4</p><p>x t y t </p><p>2t x 21</p><p>24</p><p>y x</p><p> 2</p><p>2</p><p>14</p><p>4y x</p><p>y x</p><p>(ii) State the coordinates of the focus </p></li><li><p>2 4x ay</p><p>2x at2y at</p><p>Any point on the parabola has coordinates; </p><p>where; a is the focal length </p><p>t is any real number </p><p>e.g. Eliminate the parameter to find the cartesian equation of; </p><p>21 1 , 2 4</p><p>x t y t </p><p>2t x 21</p><p>24</p><p>y x</p><p> 2</p><p>2</p><p>14</p><p>4y x</p><p>y x</p><p>(ii) State the coordinates of the focus 1</p><p>4a </p></li><li><p>2 4x ay</p><p>2x at2y at</p><p>Any point on the parabola has coordinates; </p><p>where; a is the focal length </p><p>t is any real number </p><p>e.g. Eliminate the parameter to find the cartesian equation of; </p><p>21 1 , 2 4</p><p>x t y t </p><p>2t x 21</p><p>24</p><p>y x</p><p> 2</p><p>2</p><p>14</p><p>4y x</p><p>y x</p><p>(ii) State the coordinates of the focus 1</p><p>4a </p><p>1 focus 0,</p><p>4</p></li><li><p>(iii) Calculate the parametric coordinates of the curve 28y x</p></li><li><p>(iii) Calculate the parametric coordinates of the curve 28y x2 4x ay</p></li><li><p>(iii) Calculate the parametric coordinates of the curve 28y x2 4x ay</p><p>14</p><p>8</p><p>1</p><p>32</p><p>a</p><p>a</p></li><li><p>(iii) Calculate the parametric coordinates of the curve 28y x2 4x ay</p><p>14</p><p>8</p><p>1</p><p>32</p><p>a</p><p>a</p><p>21 1 the parametric coordinates are ,16 32</p><p>t t </p></li><li><p>(iii) Calculate the parametric coordinates of the curve 28y x2 4x ay</p><p>14</p><p>8</p><p>1</p><p>32</p><p>a</p><p>a</p><p>21 1 the parametric coordinates are ,16 32</p><p>t t </p><p>Exercise 9D; 1, 2 (not latus rectum), 3, 5, 7a </p></li></ul>