  Once again, go to the Ellipse Geogebra applet and follow the instructions below.
(This will open a new window/tab in your browser. Close the window/tab to return to this lesson)

1. Set the value of 'a' at 4 and the value of 'b' at 3.
2. Move point A around the ellipse. For at least three different locations of A, write down the distances from A to F1 and F2 and add each pair of numbers.
3. Notice that the sums in each case are the same. What is the sum each time?
Interactive popup. Assistance may be required.

4. What is the relationship between a = 4 and b = 3 and the 16 and 9 in the equation?
Interactive popup. Assistance may be required.

a is the same as the x-radius and b is the same as the y-radius. 16 = x-radius2 and 9 = y-radius2 5. If the 16 and 9 in the equation switched places, how would that affect the graph of the ellipse? On the applet, change the value of a to be 3 and the value of b to be 4. Describe the changes in the graph of the ellipse and in the equation.
Interactive popup. Assistance may be required.

The ellipse now has a vertical major axis because the length of the y-radius is the longer one. This is indicated in the equation by seeing the 16 underneath the term and the 9 underneath the term. 6. In the ellipses above, what are the values of 'h' and 'k' in the equations?
Interactive popup. Assistance may be required.

h and k are both zero in these equations, placing the center at the origin. 