An architect for a golf course wants to plan a sand trap that passes between a tree and a cart path. Using these as the focus and directrix, how can the architect plan a parabolic sand trap that will be equidistant from the tree and the cart path at all times? Describe your method in full sentences.

Question

An architect for a golf course wants to plan a sand trap that passes between a tree and a cart path.  Using these as the focus and directrix, how can the architect plan a parabolic sand trap that will be equidistant from the tree and the cart path at all times? Describe your method in full sentences.

anonymous · Answer

@phi @callisto @jdoe0001 @luigi0210 @KingGeorge @ranga @compassionate @nincompoop @preetha @alltehmaffs @theeric Help me please

theeric · Answer

Do you know the meaning of "directrix" and "focus" as it pertains to a parabola?

theeric · Answer

This can help: http://www.mathwords.com/d/directrix_parabola.htm

theeric · Answer

@troyandthor ?

anonymous · Answer

Can you give me the answer than? :)

theeric · Answer

I won't give you the answer, but I'll help you work up an idea.

anonymous · Answer

Well, I need an answer haha

theeric · Answer

Sorry! I'll try to share understanding, but not an answer. Good luck!

anonymous · Answer

@theEric  The question is so that I can understand it, it's an example, not homework. Could you please answer it so I can know how to do a problem like this? Thank you!

theeric · Answer

I never give answers. I help people through the problems if I can.

Seeing the answer to a problem doesn't help you learn to tackle the problem as much as digging into it would, usually.

And I don't know what kind of answer the question is looking for, exactly, but I can see the golf scene in my head using the parabola mathematics.

anonymous · Answer

Pretend like you're my teacher. Teachers answer questions themselves, after they write them on the board..in front of all the students. Please explain to me how I would answer this.

theeric · Answer

I work $with$ people.

What I think you should know first is how a directrix and focus define a parabola. Do you know that yet?

anonymous · Answer

Man, I don't know much about parabolas.

theeric · Answer

You can get your lesson from the link I posted. http://www.mathwords.com/d/directrix_parabola.htm Now, you have the golf cart path and a tree, and you want the sand trap equidistant from them. And you need to relate that to the parabola with it's directrix and focus. After you know what the directrix and focus are, you can relate them to the problem. The sand trap will be the parabola, of course.

anonymous · Answer

Okay, I get it so far..go on..

theeric · Answer

So, what is the cart path? And what is the tree?

anonymous · Answer

Okay, so the cart path will be the directrix? And the tree is the focus?

anonymous · Answer

@theEric

theeric · Answer

Right!

anonymous · Answer

Awesome :) Is there more?

theeric · Answer

Well, I don't know what kind of answer the problem is looking for... Like, does it want you to be able to do it yourself? I don't know.

I assume that you're just suppose to come up with as many parabola related things as possible. Like, a good starting place would be at the bottom of the parabola. This point would be directly between the tree and the cart path.

If this was for an assignment, a diagram would probably be a good idea.

anonymous · Answer

Thank you for your help!

theeric · Answer

You're welcome! :)

theeric · Answer

I started on an actual method, but realized it wouldn't work.

theeric · Answer

Okay, actual method time...

So, you use a tape measurer. Start it at the tree and stretch it out a bit.|dw:1389392618633:dw|