Bob's backyard is a rectangle 40 meters by 100 meters. He uses this backyard for an exercise area for his dog. He drove two posts into the ground and fastened a rope to each post, passing the rope through the metal ring on his dog's collar. When the dog pulls on the rope while running, its path is an ellipse. If the dog can just reach all four sides of the rectangle, find the equation of the elliptical path. What is the equation of the elliptical path? (Type your answer in standard form.)