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Chapter 10: Q. 41 (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 0,3 is clockwise, and requires 1 second for a complete revolution.

Short Answer

Expert verified

The parametric equations arex=2cos2蟺迟,y=3sin2蟺迟,0鈮�t鈮�1

Step by step solution

01

Step 1. Given Information

The given ellipse is x24+y29=1

02

Step 2. Finding Parametric Equations

The rotation begins from 0,3clockwise and shown as

We can use parametric equations x=acos蝇t,y=bsin蝇t

Since one revolution requires 1 second, so T=2蟺蝇=1蝇=2蟺

Thus,x=acos蝇t,y=bsin蝇tx=2cos2蟺t,y=3sin2蟺t

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