An engineer designs a satellite dish with a parabolic cross section. The dish is 18 ft wide at the opening, and the focus is placed 5 ft from the vertex.
a) Position a coordinate system with the origin at the vertex and the x-axis on the parabola's axis of symmetry and find an equation of the parabola.
b) Find the depth of the satellite dish at the vertex.
if the vertex is at (0,0) then
x^2 = 4py has its focus at (0,p)
so now we have p = 5/4
x^2 = 5/4 y
Since the top of the dish is at x=9, y(9) = 4/5 * 81
That is the depth of the dish