Make sure to round to 2 decimal places

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 37 feet across at its opening and 12 feet deep at its center, how many feet above the vertex should the receiver be placed? (round to 2 decimal places)

Answer 1

A parabolic cross section can be drawn and oriented so that the vertex is (0,0) and the point (18.5, 12) is on the graph.

An equation of the curve is y - 0 = (1/(4p))(x - 0)²

Since the point (18.5, 12) is on the curve, 12 = (1/(4p))(18.5)²

Solve for p. The point (0, p) is the focus. The location of the focus is , in the context of this problem, the location of the reciever for the satellite dish.