Four bugs are placed at the four corners of a square with side length a . The bugs crawl counterclockwise at the same speed and each bug crawls directly toward the next bug at all times. They approach the center of the square along spiral paths.
a) Find the polar equation of a bug's path assuming the pole is at the center 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 distant traveled by a bug by the time it meet the other bugs at the center.
