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 30 feet across at its opening and 14 feet deep at its center, how many feet above the vertex should the receiver be placed? (round to 2 decimal places)

Answer 1

First consider a cross section of the receiver as a parabola of the form you have described. Place its vertex at (0,0) and face the parabola upward such that the receiver opens up.

Based on the information given about the dimensions of the receiver you should be able to come up with another point on the parabolic cross section. We know it is 14 feet deep at its center so the top edge will be somewhere along the y=14 line. Then, we know it is 30ft wide so the edge must fall at the intersection of the y=14 and x=-15 or x=15 lines.

The standard form of a parabola in this orientation is (x-h)²=4p(y-k).

Where (h,k) is the vertex of the parabola and p is the distance along the axis of symmetry to the focus, exactly what we are looking for. From here it is plug and chug! Best of luck and comment if any more guidance is needed.