SOLUTION: 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 th

Question 1204075: 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 48 feet across at its opening and 6 feet deep at its center, where should the receiver be placed?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Working the problem in 2 dimensions, we have an upward-opening parabola with vertex (0,0), with two other points at (-24,6) and (24,6).

The problem asks for where the receiver should be placed, which is at the focus of the parabola. Using the standard notation with p as the distance from the vertex to the focus, the equation of the parabola is

Determine p using (x,y)=(24,6).

p, the distance from the vertex to the focus, is 24 feet, so the focus is at (0,24).

ANSWER: 24 feet above the vertex

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