Once again, go to the Ellipse Geogebra applet and follow the instructions below.
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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?
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   Check Your Answer

   8 units
4. What is the relationship between a = 4 and b = 3 and the 16 and 9 in the equation?
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   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.
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   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?
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   h and k are both zero in these equations, placing the center at the origin.