Tracing an Ellipse

Date: 08/17/97 at 09:17:15
From: John E Gallo
Subject: Ellipse

How do you form an ellipse using 3 points?

Date: 08/22/97 at 10:38:15
From: Doctor Rob
Subject: Re: Ellipse

I think that the procedure to which you are referring is the 
following.

Two of the points are the foci of the ellipse. The third point is a
point on the curve. Use a piece of paper. At the foci, put two pins
(or tacks, or nails, or whatever). Make a loop of string just long
enough to equal the perimeter of the triangle formed by the three
points. Put it around the two pins, and put it around your pencil
point, which you locate at the third point. It should be taut. Now
move the pencil point, keeping the loop taut. It will trace out a
curve which is mathematically an ellipse.

Here's a picture:

     

F and F' are the foci, and S is the third point.  The loop is pictured 
as the triangle FF'S.

-Doctor Rob,  The Math Forum
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