A landscaper wants to plan a walkway that passes between a tree and the border of the lawn. Using these as the focus and directrix, how can the landscaper plan a parabolic path that will be equidistant from the tree and the border at all times? Describe your method in full sentences.

Question

anonymous · Answer

@wio @kohai

anonymous · Answer

I know the focus and directrix are equidistant from any point on their parabola. I'm not sure how to apply the distance formula or what not.

anonymous · Answer

the vertex will be the midpoint of the line pssing through focus and perpendicular to the border of the lawn

anonymous · Answer

Let the tree be the vertex and the border be the directrix.

anonymous · Answer

@wio 
tree can't be the vertex

anonymous · Answer

the vertex will be the midpoint of the line pssing through tree and perpendicular to the border of the lawn

anonymous · Answer

focus

anonymous · Answer

Okay.

anonymous · Answer

yup tree must be the focus

anonymous · Answer

K, I was given that. Where to from there?

anonymous · Answer

now throug the tree and parallel to the border of th lawn mark points(on both sides) which
are at distance equal to the least distance of the tree from the border of the lawn..
now join the two points as obtained above with the vertex of the drawing as obtained earlier

anonymous · Answer

Focus is above the vertex and directrix is below, correct?

anonymous · Answer

Okay. I think I have it. Any other steps?

anonymous · Answer

yup

anonymous · Answer

All done, then? :)

anonymous · Answer

Do you have time/inclination to help me with 2 more? I've halfway done with one already.

anonymous · Answer

less time dear..