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Solved: Parametric equations of ellipses Find parametric
Chapter 8, Problem 60E(choose chapter or problem)
Find parametric equations of the following ellipses (see Exercises 57-58). Graph the ellipse and find a description in terms of x and y. Solutions are not unique.
An ellipse centered at the origin with major and minor axes of length 12 and 2, on the x- and y-axes, respectively, generated clockwise
Questions & Answers
QUESTION:
Find parametric equations of the following ellipses (see Exercises 57-58). Graph the ellipse and find a description in terms of x and y. Solutions are not unique.
An ellipse centered at the origin with major and minor axes of length 12 and 2, on the x- and y-axes, respectively, generated clockwise
ANSWER:Solution 60E
Step 1:
An ellipse is generated by the parametric equations ,. 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.
The general equation of an ellipse is given by
Where is the radius of the semi-major axis and is the radius of the semi minor axis.