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

Subject: Re: Distance between a point and y = ax^2 + bx + c
From: Arturo Magidin
Date: Tue, 31 Oct 2006 20:52:36 +0000 UTC
Newsgroups: sci.math
In article <19972183.1162327554453.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx>,
Magnus  <maol9883@xxxxxxxxxxxxx> wrote:

Please quote the message you are replying to for context.


>To clarify my question. I don't understand why there are samples
>giving imaginary distances when they are real themselves as is the
>function. 

You are NOT getting "imaginary distances". What you are getting is
imaginary solutions to the auxiliary equation

dr(x)/dx = 0

(i.e., to the cubic equation that defines the DERIVATIVE of the
distance).

Since the derivative of r(x) with respct to x is a cubic, it has
either 1 or 3 real roots. In some cases, you will get 3 critical
points (when all roots are real; possibly repeated), and in some cases
you will get only 1 critical point (when one root is real and two are
complex). But these are not "imaginary distances" by any stretch. 

-- 
======================================================================
"It's not denial. I'm just very selective about
 what I accept as reality."
    --- Calvin ("Calvin and Hobbes" by Bill Watterson)
======================================================================

Arturo Magidin
magidin-at-member-ams-org


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