Question

john is constructing a satellite dish . The receiver is going to be located 15 inches above the vertex of the dish. The dish is going to be 84 inches wide. How deep will the dish be

1. The depth of the 84 inches wide satellite dish that has the receiver located 15 inches above the vertex is 29.4 inches.

### How can the equations of a parabola be used to find the depth of the dish?

The location of the receiver = 15 inches above the vertex
Width of the dish = 84 inches
The receiver of a satellite dish is normally located at the focus (focal point).
Taking the shape of the satellite dish as a parabola, and writing the equation of the parabola as = 4•a•y, we have;
Coordinates of the focus = (0, a)
Where;
a = The distance of the focus above the vertex
Therefore;
a = 15 inches
The dish is horizontally spaced equally about the vertex.
The farthest point horizontally from the vertex, X, of the dish corresponds to the furthest vertically from the vertex, which is the maximum depth or height, Y.
At the maximum height, from the vertex, Y, (farthest point, vertically from the vertex), we have;
X = 84 ÷ 2 = 42
Which gives;
42² = 4 × 15 × Y
Y = 42² ÷ (4 × 15) = 29.4
• The depth of the dish is 29.4 inches