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Chapter 10: Q. 39 (page 695)

In Problems 39 鈥� 42, find parametric equations for an object that moves along the ellipsex24+y29=1with the motion described.

The motion begins at 0,2, is clockwise, and requires 2 seconds for a complete revolution.

Short Answer

Expert verified

The parametric equation isx=2cos蟺迟,y=-3sin蟺迟,0鈮�t鈮�2

Step by step solution

01

Step 1. Given Information

We are given an ellipse x24+y29=1

The graph of ellipse is shown as

02

Step 2. Finding Parametric Equation

The parametric equation is x=acos蝇t,y=bsin蝇t

x=2cos蝇t,y=-3sin蝇t

Since one revolutions requires 2 seconds, the period is T=2蟺蝇=22蝇=2蟺蝇=蟺

As a result,x=2cos蟺t,y=-3sin蟺t

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