A satellite dish is the shape of a paraboloid. The dish is 42 inches wide, and 10 inches deep. How many inches should the receiver be located from the vertex for optimal

Answer 1

a side view shows a parabola with vertex a t (0,0), so
y = ax^2
y(21) = 10, so a = 10/21^2
y = 10/441 x^2
Now recall that the parabola
x^2 = 4py has focus at (0,p)
So, since our equation is
x^2 = 441/10 y, p = 441/40
So the receiver should be placed 11.025 inches from the vertex