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)*

- Set the value of 'a' at 4 and the value of 'b' at 3.
- Move point A around the ellipse. For at least three different locations of A, write down the distances from A to F
_{1}and F_{2}and add each pair of numbers. - Notice that the sums in each case are the same. What is the sum each time?
- What is the relationship between
*a*= 4 and*b*= 3 and the 16 and 9 in the equation? - 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. - In the ellipses above, what are the values of '
*h*' and '*k*' in the equations?