Question

A satellite dish is shaped like a paraboloid of revolution. this means that it can be formed by rotating a parabola around its axis of symmetry. the receiver is to be located at the focus. if the dish is 14 feet across at its opening and 2 feet deep at its center, where should the receiver be placed? enter your answer rounded to two decimal places.

Answer 1

The receiver of a parabolic satellite dish should be placed at the focus of the parabola, which for the dish described, is 2 feet above the bottom of the dish.

Step-by-step explanation:

To determine where the receiver should be placed in a paraboloid satellite dish, we need to know the position of the focus of the parabola. The dimensions given are that the dish is 14 feet across, which is the diameter, so the radius is 7 feet, and the depth or height of the dish at its center is 2 feet.

In the standard form equation y = (1/(4f))x^2 for a parabola, f represents the focus. Given that the depth of the dish is 2 feet, this means that f = 2 feet, because for a parabola, the depth (vertex to the focus) is equal to the focus distance from the vertex. The vertex, in this case, will be the bottom of the dish, and the receiver needs to be placed at the focus, which is 2 feet above the vertex. Hence, the receiver should be placed 2 feet from the bottom of the dish.