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# Show that the ellipse x = a cos t, y = b sin t, a > 0, has

ISBN: 9780321717399 65

## Solution for problem 18E Chapter 12.4

University Calculus: Early Transcendentals | 2nd Edition

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Problem 18E

Show that the ellipse x = a cos t, y = b sin t, a > 0, has its largest curvature on its major axis and its smallest curvature on its minor axis. (As in Exercise 17, the same is true for any ellipse.)17. Show that the parabola has its largest curvature at its vertex and has no minimum curvature. (Note: Since the curvature of a curve remains the same if the curve is translated or rotated, this result is true for any parabola.)

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