Focus of parabola, checking my answer.

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Homework Help Overview

The problem involves determining the distance from the vertex to the focus of a parabolic antenna, given its dimensions of a 32-foot diameter and a depth of 4 feet. The original poster expresses uncertainty regarding their answer of 16 feet, which they initially changed before submitting an online test.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the interpretation of the dimensions, with one suggesting a possible reversal of the depth and diameter. There is also an exploration of the relationship between the variables involved in the problem.

Discussion Status

The discussion is ongoing, with participants questioning the original poster's understanding of the problem setup. Some clarification has been provided regarding the interpretation of the dimensions, but no consensus has been reached on the correct answer.

Contextual Notes

There appears to be confusion regarding the definitions of depth and diameter in the context of the parabolic shape, which may affect the calculations. The original poster's change of answer before submission is also noted as a point of concern.

jkristia
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I just had this question in an online test I took, and first I had 16ft, but for some unknown reason I chose to change it to 64ft right before I submitted the test, and of course I got it wrong. So I just want to confirm the answer is indeed 16ft.

Homework Statement



A parabolic antenna has a diameter of 32 feet and is 4 foot deep. How far is the focus from the vertex?

Homework Equations


The Attempt at a Solution



attachment.php?attachmentid=44719&stc=1&d=1330896961.png


My answer - Focus for this parabola is (0, a), so (0, 16) or 16ft from vertex
 

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I think you have the depth and the diameter reversed.
 
Hmm, not sure I understand why you think that.

The way I read this is when x = 16, then y = 4, (the 'depth' 16 feet out to the bottom of the vertext is 4 feet), but maybe I misunderstood something.
 
jkristia said:
Hmm, not sure I understand why you think that.

The way I read this is when x = 16, then y = 4, (the 'depth' 16 feet out to the bottom of the vertext is 4 feet), but maybe I misunderstood something.

Never mind. I had my two variables interchanged. You are correct.
 

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