Question

A satellite dish is shaped like a paraboloid of revolution. The signals that emanate from a satellite strike the surface of the dish and are reflected to a single point, where the receiver is located. If the dish is 10 feet across at

its opening and 4 feet deep at its center, at what position should the receiver be placed?

Short answer

The position of receiver will be 1.562 ft .

Step-by-step solution

Step 1. Given information .

Consider the given distance from the base and depth .

Step 2. Equation of parabola used.

The equation of the parabola is $x^2=4ay$,the vertex of the parabola is at origin and its focus is on the y positive axis .

Here ,$x=\frac{10}{2}=5$and $a=4$.

Substitute the values in equation of parabola .

$$\begin{gathered} x^2=4ay \\ {\left(5\right)}^2=4·4·y \\ y=\frac{25}{16} \\ y=1.562 \end{gathered}$$

Therefore the receiver should be located 1.562 ft from the base of the dish .