Figure A shows a satellite dish with a radio receiver located at the focus of the parabola. The radio rays are reflected from the parabolic surface and concentrated at the focus. This focusing and amplification property of parabolic reflectors is also used for solar heating and generating solar electricity.

figure B defines the distance, , of the focus from the bottom of the dish, and the diameter, , of the dish.

Suppose you wanted to design a parabolic dish with a depth, , of 1 meter and a radius of 5 meters. Where would the focus be located?

The basic equation of a parabola is ax^2

The location of the focus will be at f = 1/(4)

Since we know that the point (5, 1) is on the curve of the parabola, that means that we can begin solving for for this particular dish.

1 = (5)^2 therefore = 1/25

We can now put the value for in our formula for the location of the focus.

= 1/(4)

= 1/(4/25)

= 25/4

= 6 1/4

Therefore our focus is at 6 1/4 meters above the bottom of the dish and this is where we should place our receiver. Let’s design a few parabolic reflectors that we can use to reflect and concentrate sound waves, or sunlight!