A satellite dish is shaped like a paraboloid of revolution. The signals that emanate from a satellite strike the surface of the dish and are reflected to a single point, where the receiver is located. If the dish is 14 feet across at its opening and 5 feet deep at its center, at what position should the receiver be placed? The receiver should be placed feet from the base of the dish, along its axis of symmetry. (Type an exact answer in simplified form.)

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A: Here I am attaching image so that you understand each and every step.

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.