A cake maker has rectangular boxes measuring $40 \mathrm{~cm}$ in length and 20 $\mathrm{cm}$ in width. The four vertices of the rectangle are (0,0), (0,20), (40,20), (40,0). She often receives orders for cakes in the shape of an ellipse, and wants to determine the largest possible cake that can be made to fit inside the rectangular box.

State the coordinates of the center of the cake in the form $(a, b)$.

Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.
Question: A cake maker has rectangular boxes measuring $40 \mathrm{~cm}$ in length and 20 $\mathrm{cm}$ in width. The four vertices of the rectangle are (0,0), (0,20), (40,20), (40,0). She often receives orders for cakes in the shape of an ellipse, and wants to determine the largest possible cake that can be made to fit inside the rectangular box.

State the coordinates of the center of the cake in the form $(a, b)$.

Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.
Question: A cake maker has rectangular boxes measuring $40 \mathrm{~cm}$ in length and 20 $\mathrm{cm}$ in width. The four vertices of the rectangle are (0,0), (0,20), (40,20), (40,0). She often receives orders for cakes in the shape of an ellipse, and wants to determine the largest possible cake that can be made to fit inside the rectangular box.

State the coordinates of the center of the cake in the form $(a, b)$.
