Question

Constructing a TV Dish - A cable TV receiving dish is in the shape of a paraboloid of revolution. Find the location of the receiver, which is placed at the focus, if the dish is 6 feet across at its opening and 2 feet deep.

Short answer

The location of the receiver is at 1.12 ft .

The image of satellite shown below .

Step-by-step solution

Step 1. Given information .

Consider the given distance of dish and depth .

Step 2. Equation of parabola used.

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

Here role="math" localid="1647017339617" $x=\frac{6}{2}=3$,and $y=2$.

Substitute the values in given formula .

$$\begin{gathered} x^2=4ay \\ {\left(3\right)}^2=4·2·a \\ a=\frac{9}{8} \\ a=1.12 \end{gathered}$$

Therefore the location of the receiver is at 1.12 ft .

Step 3. Plot the graph .

The graph of the receiver shown below .