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

anonymous · Answer

@ganeshie8

anonymous · Answer

The cart path can be a directix and tree the focus

ganeshie8 · Answer

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anonymous · Answer

I would help but I have no clue.

ganeshie8 · Answer

Suppose the vertex of parabolic sand trap is at origina and the parabola opens up.
Say $F = (0, a)$, then the equation of drectrix line would be $y = -a$.

Let $P(x,y)$ be any point on the parabola and $M$ be the perpendicular from $P$ to the directix line : 
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