Re: Distance between a point and y = ax^2 + bx + c

In article <20061031234246.931$lw@xxxxxxxxxxxxxx>,
David W. Cantrell <DWCantrell@xxxxxxxxxxx> wrote:
magidin@xxxxxxxxxxxxxxxxx (Arturo Magidin) wrote:
In article
<1235297.1162325667272.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx>, Magnus
<maol9883@xxxxxxxxxxxxx> wrote:
[snip]
I'm trying arbitrary functions y = ax^2 + bx + c with arbitary points
to find the closest point between.

Given a point (x0,y0), some parabolas have a unique "closest point" to
it. Some have more than 1; for example, the closest points to (0,1) on
the parabola x=y^2 are (0,0), (1,1), and (-1,1), all of them distance
1.

Three points?! There are at most _two_ closest points.

Quite right. My mistake there.

--
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"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes" by Bill Watterson)
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Arturo Magidin
magidin-at-member-ams-org

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