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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?

 Apr 24, 2019
 #1
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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

 

 

cool cool cool

 Apr 24, 2019

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