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2 EXAMPLE 4 If the ellipse defined by the equation below is rotated counterclockwise through an angle 3/10 about the origin, find a polar equation and graph the resulting ellipse. 10 r = 3 - 2 cos(0) SOLUTION We get an equation of the rotated ellipse by replacing with in the 2 equation above. So the new equation is We use this equation to graph the rotated ellipse in the figure. Notice that the ellipse has been rotated about its left focus at the origin.

2 EXAMPLE 4 If the ellipse defined by the equation below is rotated counterclockwise through an angle 3/10 about the origin, find a polar equation and graph the resulting ellipse. 10 r = 3 - 2 cos(0) SOLUTION We get an equation of the rotated ellipse by replacing with in the 2 equation above. So the new equation is We use this equation to graph the rotated ellipse in the figure. Notice that the ellipse has been rotated about its left focus at the origin.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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6 2 EXAMPLE 4 If the ellipse defined by the equation below is rotated counterclockwise through an angle 3π/10 about the origin, find a polar equation and graph the resulting ellipse. r = 10 3 - 2 cos(0) SOLUTION We get an equation of the rotated ellipse by replacing with in the 2 equation above. So the new equation is We use this equation to graph the rotated ellipse in the figure. Notice that the ellipse has been rotated about its left focus at the origin.
Transcribed Image Text:6 2 EXAMPLE 4 If the ellipse defined by the equation below is rotated counterclockwise through an angle 3π/10 about the origin, find a polar equation and graph the resulting ellipse. r = 10 3 - 2 cos(0) SOLUTION We get an equation of the rotated ellipse by replacing with in the 2 equation above. So the new equation is We use this equation to graph the rotated ellipse in the figure. Notice that the ellipse has been rotated about its left focus at the origin.
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