Conics Instructional Unit
Day 4 - Introduction to Ellipses
by
Mandy Stein
Ellipse
The locus of all points P(x,y) such that the sum of the distance from P to two fixed points, called foci, are constant.
To construct an ellipse in Geometer’s Sketchpad:
1. Construct a circle. The center of the circle is one of the foci
2. Construct a point on the circle
3. Construct a point inside the circle, this is the second foci
4. Construct a line segment connecting the second foci and the point on the circle
5. Construct the perpendicular bisector of this segment
6. Construct a line segment connecting the first foci (the center of the circle) to the point on the circle
7. Tracing the perpendicular bisector while moving the point around the circle will produce the locus of all points such that the sum of the distance from P to two fixed points
If the only the point is traced, this picture results
