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Problem: A website describes how to make a parabolic dish with a wok and a microphone attached to the focal point. You have a wok 22 inches wide (shown as vertical on the paper) and 8 inches deep (shown as horizontal). Write an equation that represents the cross section of the wok. Find the location of the microphone as well.

Background info (for anyone asking if I attempted problem): For this one, it was asking to find the focus. I thought the focus was (8,0), so in x = 1/4p * y^2, I subbed in 8 as p and got x = 1/32 y^2. However, one of the points supposed to be on the graph was (8,13), which wasn't on the equation I got. So, I'm sure what I did was wrong.

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  • $\begingroup$ Where is the origin? If it is the vertex of the parabola with the $x$ axis the axis of the parabola, then the point should be $(8,11)$. Why should the focus be at the exit plane? You should choose $p$ so that $(8,11)$ is on the graph. That will tell you where the focus is. $\endgroup$ – Ross Millikan Jan 7 '17 at 20:30
  • $\begingroup$ Ross, the origin is shown to be at (0,0). And with all of the given information, how would I find the focus? $\endgroup$ – advanced_file_type Jan 7 '17 at 20:34
  • $\begingroup$ I don't see a link to the picture or I would have pasted it in. First you find the equation in the form $x=Ay^2$ from the point you have. Then you have been told that $A=\frac p4$ $\endgroup$ – Ross Millikan Jan 7 '17 at 20:54
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First you find the equation in the form $x=Ay^2$ from the point you have. Then you have been told that $A=\frac p4$

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