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The city planning board has set aside funds to build a bridge going north and south across the Newton River. To save money, they have agreed to build the shortest bridge possible. A map for the -mile wide city is shown below. The equations below represent the river banks where is the number of miles east of City Hall and y is the number of miles north of City Hall. Find the location for the shortest bridge that will span the Newton River.

North Bank:

South Bank:

At any give value of , the distance between the North and South Banks is: