and Parametric Equations

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Presentation transcript:

and Parametric Equations 13.1 Plane curves and Parametric Equations Rita Korsunsky

Parametric Equations For example :

Example 1 Sketch the graph of a curve with parametrization: Method 1 Make a Chart and graph 3 -1 y 4 2 1 -2 x t Method 2 Eliminate the parameter t and graph The graph is the same as the graph we got by using method 1. Arrows on graph show the direction in which particle traces the curve as t increases from –1 to 2.

Example 2   t = 0 (1,0) x2 + y2 = 1 t t = 2 t = 0 t = 

 t = t = 0 t= (1, 0) (0, -1) Example 3

Example 4 Sketch the graph and indicate the orientation • 0 Start t = 0 (1, 1) t = 1 (t, t) Particle moves from left to right, and covers only the right hand portion of the parabola.