Answer to Question #54770 in Calculus for Cameron

Question #54770

Four bugs are placed at the four corners of a square with side length a. The bugs crawl counter-clockwise at the same speed and each bug crawls directly toward the next bug at all times. They approach the centre of the square along spiral paths.
a) Find the polar equation of a bug's path assuming the origin (pole) is at the centre of the square. (Use the fact that the line joining one bug to the next is tangent to the bug's path).
b) Find the distance travelled by a bug by the time it meets the other bugs at the centre.

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