Constructing an Ellipse
- Tabitha McAfee
Find the locus that will create an ellipse. An ellipse is the set of points such that the sum of the distances from two points is constant.
1) Create a circle with center at A with defined radius d. 2) Create another circle centered at B and with radius a-d. 3) Move the slider until the circles intersect at two points. Label those two points C and D. 4) Create segments AC, AD, BC and BD. 5) Unselect the circles so that they do not show up. 6) Right click on C and D and turn on the trace. 7) Move the slider around to see the points C and D "create" an ellipse.
Given the definition of an ellipse (see above) why did we construct the circles in this way? Hint: How did we define our radii?