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 40 inches wide and 20 inches deep, how far from the vertex should the microphone be placed?

Answer 1

The vertex of the parabola is located midway between its focus and directrix, and the directrix is located 20 inches from the vertex. Therefore, the focus is also located 20 inches from the vertex.

Using the formula for the distance between a point on the parabola and its focus (p), we can solve for p:

p = (1/4)w = (1/4)(40 inches) = 10 inches

Therefore, the microphone should be placed 20 + 10 = 30 inches from the vertex of the parabolic dish.