Suppose you have a satellite dish 10 feet across and 2 feet deep. How far up from the center of the satellite dish should you put the receiver?

Question

Suppose you have a satellite dish 10 feet across and 2 feet deep. How far up from the center of the satellite dish should you put the receiver?

Answer 1

If you take your parabola to be symmetric with the y-axis with (0,0) as the vertex, then with a width of 10, the unit extends 5 & -5 on the x-axis and y=2.

the equation of the parabola is y=a(x-h)2 + k where h,k are the vertex coordinates which are (0,0).

So, y=ax2. To find a, we substitute y=2 at x=5 to obtain 2=a(5)2 or a=2/25 and y = (2/25)x2

the coordinates of the focus (where the receiver should be) are h, k+1/4a or (0, 25/8) or (0,3.125)