+68 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?
+128474 If the width of the parabola is 60 and the height is 30,......by letting the vertex lie at the origin, then the point (30, 30) is on the graph..........so we have the follwing function where p is the distance from the vertex to to focal point
y = ( x ) ^2 / [4p] and since the point (30,30) is on the graph,we have
30 = (30)^2 / [4p] divide both sides by 30
1 = 30 / [4p] multiply both sides by 4p
4p = 30 divide both sides by 4
p = 7.5 the focal point is 7.5 units above the vertex = (0, 7.5)
