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.

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