The reflecting dish of a parabolic microphone has a cross-section in the shape of a parabola. The microphone itself is placed on the focus of the parabola. If the parabola is 60 inches wide and 30 inches deep, how far from the vertex should the microphone be placed?

Answer 1

If we set the vertex at (0,0) then the curve goes through (30,30)

y = 1/30 x^2
x^2 = 30y

Since the parabola x^2 = 4py has its focus at y=p, 4p=30 and the mic should be 15/2 inches up from the vertex.