9. Margaret has some left over carpet after she finished remodeling her house. She would like to make an elliptical rug with the leftover carpet. She sketches two foci 31 inches from the center of the ellipse on a piece of paper. In order to determine the shape of the ellipse, she loops a pencil through a string that is 77 inches long and fixes the ends of the string at two cocci. Determine the longest and shortest lengths of the elliptical rug.