Question

Satellite Dish- 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 receiver should be located$1.5625$ft from the base of the dish along its axis of symmetry .

Step-by-step solution

Step 1. Given information .

Consider the given dimensions .

Step 2. Find at what position should the receiver be placed .

The vertex of the parabola is at the origin and its focus is on the positive y axis .

The form of the equation of the parabola is $x^2=4ay$and its focus is at $\left(0,a\right)$since point $\left(5,4\right)$is a point on the graph .

Substitute the value of x ,y in the equation of parabola .

$$\begin{gathered} x^2=4ay \\ {5}^2=4·a·4 \\ a=\frac{25}{16} \\ a=1.5625 \end{gathered}$$