 We can define both elements of the ordered pair, (x, y), in terms of another variable, t, called a parameter.  Example: Given and, a) Find the points.

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Presentation transcript:

 We can define both elements of the ordered pair, (x, y), in terms of another variable, t, called a parameter.  Example: Given and, a) Find the points determined by t = -3, -2, -1, 0, 1, 2, & 3. b) Find a direct relationship between y and x and determine whether the parametric equations determine y as a function of x. c) Graph the relationship in the xy-plane.

 In order to graph parametric equations, you must change your mode from functions to parametric. Hit the “Mode” key. On the 4 th line, shift to PAR.  Example: Given and, a) Use a graphing calculator to find the points determined by t = -3, -2, -1, 0, 1, 2, & 3. b) Use a graphing calculator to graph the relation in the xy-plane. c) Is y a function of x? d) Find an algebraic relationship between x and y.

 Example: Graph and on the following intervals… a) b)

 Solve for one variable. Substitute into 2 nd equation. Simplify.  Example: Eliminate the parameter and identify the graph of the parametric curve: a) b)

 Write a parametric equation for a circle with radius of 7 and center at (-3, 5).

 Example: Find a parametrization for the line through the points (4,1)when t = 0 and (19, 26) when t = 5.