Rotation and Dilation from Parametric Equations Project: Here are the general parametric

Chapter 12, Problem 21

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Rotation and Dilation from Parametric Equations Project: Here are the general parametric equations for an ellipse centered at the origin with x- and y-radii a and b, respectively, that has been rotated counterclockwise through an angle of . Assume that t is in the range of [0, 2 ]. x = (a cos ) cos t + (b cos( + 90)) sin t y = (a sin ) cos t + (b sin( + 90)) sin t a. Use the rotation matrix to show how these equations follow from the unrotated ellipse equations x = a cos t y = b sin t b. A particular ellipse has parametric equations x = 3 cos t 2 sin t y = 5 cos t + 1.2 sin t Calculate algebraically the major and minor radii and the angle that one of the axes makes with the x-axis. Show by graphing that your answers are correct.