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Topic: [ap-calculus] Going crazy
Replies: 2   Last Post: Oct 17, 2012 1:48 PM

 Messages: [ Previous | Next ]
 John Hanna Posts: 106 Registered: 1/8/11
RE: [ap-calculus] Going crazy
Posted: Oct 15, 2012 9:40 PM

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I think the 'b' and the 'c' terms matter, too.

John Hanna
jehanna@optonline.net
www.johnhanna.us
T3 - Teachers Teaching with Technology
"the future isn't what it used to be."

-----Original Message-----
From: John Losse [mailto:jlosse@me.com]
Sent: Monday, October 15, 2012 4:14 PM
To: AP Calculus
Subject: RE:[ap-calculus] Going crazy

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for the new AP Calculus
Teacher Community Forum at
https://apcommunity.collegeboard.org/getting-started
and post messages there.
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Did anyone notice that the intersection of the two tangent lines is the
midpoint of the line segment joining the vertices of the parabolas? This
leads to the following conjecture and an alternate way to approach the
problem:

which are "a" and "-a" respectively, are symmetric with respect to the
midpoint of their vertices.

A line through this midpoint which is tangent to one parabola will, by the
symmetry, be tangent to the other.

The common tangents can therefore be found by the slightly different process
of finding the tangents to a parabola from an external point.
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