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 12 feet across at its opening and 2 feet deep at its​ center, at what position should the receiver be​ placed?

Answer 1

Answer:

18feet

Explanation:

We need to find the distance,c between the vertex and the focus.

For a vertical parabola:

$y=\frac{0.25}{c}(x-h)^2+k$

#If we place our parabola at the center, the expression changes to:

$y=\frac{0.25}{c}x^2$

The points of the parabola are given as (12,2), substitute in our equation to find c:

$y=\frac{1}{4c}x^2\\\\2=\frac{1}{4c}\times12^2\\\\c=12$

Hence, the receiver should be placed at 18ft