Focus of parabola, checking my answer.

In summary, the question is about the distance between the focus and the vertex of a parabolic antenna with a diameter of 32 feet and a depth of 4 feet. Initially, the answer given was 16 feet, but it was changed to 64 feet before submission, resulting in an incorrect answer. The correct answer is indeed 16 feet.
  • #1
jkristia
54
0
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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  • #2
I think you have the depth and the diameter reversed.
 
  • #3
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.
 
  • #4
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.
 

Related to Focus of parabola, checking my answer.

1. What is the focus of a parabola?

The focus of a parabola is a fixed point on the interior of the parabola that is equidistant from all points on the parabola. It is also the point where all of the parabola's reflected light rays converge.

2. How do you find the focus of a parabola?

To find the focus of a parabola, you can use the formula (h, k + 1/4a), where h and k are the coordinates of the vertex and a is the coefficient of the squared term. Alternatively, you can also use the distance formula to find the distance between the vertex and any point on the parabola, which will be equal to the distance between the focus and that same point.

3. What is the significance of the focus in a parabola?

The focus is significant because it determines the shape and orientation of the parabola. It is also used to calculate important features of the parabola, such as its directrix and focal length.

4. How can I check if my answer for the focus of a parabola is correct?

You can check your answer by using the distance formula to find the distance between the focus and any point on the parabola. If the distance is equal, then your answer is correct. Additionally, you can also graph the parabola and visually check if the focus is equidistant from all points on the curve.

5. Can a parabola have more than one focus?

No, a parabola can only have one focus. This is because the focus is a fixed point that is determined by the shape and orientation of the parabola. If the focus were to change, the shape of the parabola would also change.

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