Drawing An Ellipse

Date: 11/24/97 at 03:53:03
From: Andy Liu
Subject: Draw an ellipse with only a straight edge and compass

Hello Dr. Math,

I am stuck on a homework problem. I would like to know how to draw an 
ellipse with only a straightedge and a compass.

Thank you,

Andy

Date: 11/24/97 at 11:51:54
From: Doctor Rob
Subject: Re: Draw an ellipse with only a straight edge and compass

You cannot draw an ellipse with a straightedge and compass alone.  
The curved line which constitutes the ellipse is not the arc of any 
circle, and no part of it is a straight line.

You can plot lots of points on the ellipse with these tools, but to
draw the curve you will have to either use an additional tool or do
it freehand. To plot points proceed as follows.

Pick two points A and B in the plane which will be the foci of the
ellipse. Separately draw a line segment CD whose length is greater
than the distance AB. Pick any point P between C and D on CD. Set
your compass to length CP. Draw a circle with center A and radius CP.
Now set your compass to length DP. Draw another circle with center B
and radius DP. The points where the two circles intersect will be
points on the ellipse. Repeat this for several new choices of P.  
For each you will get 2, 1, or 0 points on the ellipse.

When you think you have enough points, draw the ellipse freehand.

-Doctor Rob,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/