# 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 step-by-step instructions

The above animation is available as a printable step-by-step 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.