9_6 (3_5) - Plane Curves and Parametric Equations

9_6 (3_5) - Plane Curves and Parametric Equations -...

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4/27/2010 1 Plane Curves and Parametric Equations Calculus II Section 9.6 (3.5) Definition of a Plane Curve If f and g are continuous functions of t on an interval I, then the equations x = f(t) and y=g(t) are called parametric equations and t is called the parameter . The set of points (x,y) obtained as t varies over the interval I is called the graph of the parametric equations. Taken together, the parametric equations and the graph are called a plane curve , denoted by C . Example Compare 1) x = t 2 + 1, y=2t 2 – 1 2) x = 1 – t 2 , y = -1 – 2t 2 Eliminating the Parameter Another way to find out information about a specific plane curve is to eliminate the
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Unformatted text preview: parameter and find a rectangular equation that represents the same graph. When you do this be careful to restrict the range and domain of the new equation accordingly. Examples Sketch the curves. 1) 2) 2 3 ,-= = t y t x t y t x sin 2 5 , cos 2 3-= + = Smooth Curves A curve C represented by x=f(t) and y=g(t) is called smooth f’ and g’ are continuous on I and not simultaneously 0, except possible at the endpoints of I. The curve C is called piecewise smooth if it is smooth on each subinterval of some partition of I. PDF created with FinePrint pdfFactory trial version http://www.pdffactory.com...
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This note was uploaded on 01/13/2012 for the course MATH 2564 taught by Professor Pamelasatterfield during the Spring '12 term at NorthWest Arkansas Community College.

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