
Finding the foci of a given ellipse
This shows how to find the two
foci
of an
ellipse
given its width and height
(major and minor axes).
This can be used to find the two focus points when you are planning to draw an ellipse using the
string and pins method.
Uses a compass, no measuring is used. A Euclidean construction.
Printable stepbystep instructions
The above animation is available as a
printable stepbystep instruction sheet, which can be used for making handouts
or when a computer is not available.
Proof
The image below is the final drawing above with the some items added.

Argument 
Reason 
1 
Line segments CF2 and OB are
congruent 
Compass width set from OB used to draw CF2 
2 
Line segments CF2 and CF1 are
congruent 
Drawn with the same compass width. 
3 
CF1 + CF2 = AB 
OB is half AB 
4 
F1 and F2 are the foci of the ellipse 
From the definition of an ellipse.
From any point C on the ellipse, the sum of the distances from C to each focus is equal to the major axis length. 
 Q.E.D
Try it yourself
Click here for a printable worksheet containing an ellipse drawing problem.
When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.
Other constructions pages on this site
Lines
Angles
Triangles
Right triangles
Triangle Centers
Circles, Arcs and Ellipses
Polygons
NonEuclidean constructions
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