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## Parametric Representation of Curves

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**Parametric Representation of Curves**Lesson 9.4**Parametric Representation**• Define variables (x,y) to be each functions of some other variable • usually t for time • Sox = g(t) and y = h(t) • The calculator has a parametric mode**Parametric Mode on Calculator**• Note the appearance ofthe Y= screen • must use t • must have both a functionfor x and for y • Note also thechange in the window specs**Eliminate the Parameter**• Use substitution • Solve for t • Set results equalto each other • Solve for y**Eliminate the Parameter**• Try this one**Eliminate the Parameter**• Use Trig Identities • What is this figure?**Eliminate the Parameter**• Use other relationships: • consider y = ln x**Finding Derivatives**• Given x = g(t) y = h(t) • Then • Try**Finding Derivatives**• For… we get • To evaluate, substitute a specific t in • Also possible to eliminate the parameter with substitution**Area under the Parametric Curve**• Given x = x(t) y = y(t) • Then a=x(t1) b=x(t2)**Area under the Parametric Curve**• Try this:**Assignment**• Lesson 9.4 • Page 659 • Exercises:5, 9, 13, 15, 19, 23, 25, 29, 31, 33, 35, 37, 41