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 9 inches deep, how far from the vertex should the microphone be placed?

6 in , 8 in, 16 in, , 4 in

Question

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 9 inches deep, how far from the vertex should the microphone be placed?

6 in   ,     8 in,      16 in,           ,   4 in

driftracer305 · Answer

@ganeshie8

driftracer305 · Answer

@phi   @campbell_st

mackenzie2013 · Answer

4 inches.

mackenzie2013 · Answer

Place the vertex at the origin. Then the parabola has equation 

4py = x² 

4p(9) = 144 

p = 4 in

mackenzie2013 · Answer

I have no comment..

mackenzie2013 · Answer

My lips are sealed. Looks like you're the one who googled it :P

driftracer305 · Answer

lol........... Ms. Smarty @Mackenzie2013 ..........  good one..!! haha

mackenzie2013 · Answer

Thank ya! haha

driftracer305 · Answer

uhh @campbell_st ....... pls help?!??

campbell_st · Answer

the solution you have been given is correct... 

here is a diagram showing why... 

|dw:1405499572644:dw|

so the general form I use is 

$$x^2 = 4ay$$

where a is the focal length... or distance from the vertex to the focus... 

so substituting x = 12 and y = 9 it becomes

$$144 = 4 \times a \times 9$$

solving for a will give the focal length and subsequently how far above the vertex
the focus is. 

hope it makes sense.