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 24 inches wide and 4 inches deep, how far from the vertex should the microphone be placed?

ChaserColour Apr 24, 2019

#1**+2 **

Let the vertex be at (0,0)

And the point (12, 4) is on the parabola.....so we have the form

y = mx^2 and we know that

4 = m(12)^2

4 = 144m divide both sides by 144

1/36 = m

So.....the form is

y = (1/36)x^2

36y = x^2

And 36 = 4a divide both sides by 4

9 = a

So...the focus is given by (0, 0 +a) = (0, 0 + 9) = (0, 9)

So.....the microphone should be placed 9 inches from the vertex

CPhill Apr 24, 2019