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Calculus / Calculus: Early Transcendentals 1 / Chapter 10.1 / Problem 57E

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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Ellipses An ellipse (discussed in detail in Section 10.4)

Chapter 8, Problem 57E

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QUESTION:

Ellipses An ellipse (discussed in detail in Section 10.4) is generated by the parametric equations x = a cos t, y = b sin t. If 0 < a < b, then the long axis (or major axis) lies on the y-axis and the short axis (or minor axis) lies on the x-axis. If 0 < b < a, the axes are reversed. The lengths of the axes in the x- and y-directions are 2a and 2b, respectively. Sketch the graph of the following ellipses. Specify an interval in t over which the entire curve is generated.

x = 4 cos t, y = 9 sin t.

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QUESTION:

Ellipses An ellipse (discussed in detail in Section 10.4) is generated by the parametric equations x = a cos t, y = b sin t. If 0 < a < b, then the long axis (or major axis) lies on the y-axis and the short axis (or minor axis) lies on the x-axis. If 0 < b < a, the axes are reversed. The lengths of the axes in the x- and y-directions are 2a and 2b, respectively. Sketch the graph of the following ellipses. Specify an interval in t over which the entire curve is generated.

x = 4 cos t, y = 9 sin t.

ANSWER:

Solution 57EStep 1: An ellips

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