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Chapter 10: Q. 40 (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 counterclockwise, and requires 1 second for a complete revolution.

Short Answer

Expert verified

The parametric equation isx=-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

The graph is shown in the figure

02

Step 2. Finding Parametric Equations

The ellipse is rotated at 0,3and shown as

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

The ellipse is rotated towards -2,0.So, a=-2,b=3

Since one revolution requires 1 seconds, the period is 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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