Objectives
After completing this chapter, you should be able to:
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Describe the motion of a point in the plane with a pair of parametric equations \(x = f(t)\) and \(y = g(t)\text{,}\) and understand the parameter \(t\) as recording when the point visits each place on the curve.
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Sketch a parametric curve from a table of values, and indicate the direction of increasing \(t\) in which the curve is traced.
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Find parametric equations for common curves, such as lines, circles, and ellipses, and eliminate the parameter to recover a Cartesian equation when possible.
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Model the motion of a projectile with parametric equations, and derive the equation of its parabolic trajectory.
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Distinguish the intersection points of two parametric curves from their collision points, where two moving objects reach the same place at the same time.
