9.5. If f and g are continuous functions of t on an interval I, the set of ordered pairs (f(t), g(t)) is a plane curve, C. The equations given by x =

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Presentation transcript:

9.5

If f and g are continuous functions of t on an interval I, the set of ordered pairs (f(t), g(t)) is a plane curve, C. The equations given by x = f(t) and y = g(t) are parametric equations for C, and t is the parameter. Definition of a Plane Curve

Sketch the curve given by the parametric equations x = t 2 – 4 and y = t/2 with -2 ≤ t ≤ 3. Example 1

Do example 2 on graphing calculator. Pg. 670

Yes! To eliminate the parameter, solve for t in one of the equations and substitute this into the second equation. Can we get rid of the parameter?

Identify the curve represented by: Example 2

A)Find a set of parametric equations to represent the graph of y = 1 – x2 using parameters 1) t = x and 2) t = 1 – x. B)Find a set of parametric equations to represent the graph of y = 4x – 3. Example 3