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Chapter 10: Q.42 (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 2,0, is counterclockwise, and requires 3 seconds for a complete revolution.

Short Answer

Expert verified

The parametric equations are x=2cos2蟺3t,y=3sin2蟺3t,0鈮�t鈮�3

Step by step solution

01

Step 1. Given Information

The given ellipse is x24+y29=1

The graph is shown as

02

Step 2. Finding Parametric Equations

The motion begins at2,0 is counterclockwise,

We can use x=acos蝇t,y=bsin蝇t

Since one revolutions requires 3 seconds

T=2蟺蝇=3

蝇=2蟺3

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

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