Explore the relationship between a and b and the shape of the ellipse using the following applet:

Ellipse Geogebra Applet
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After exploring the applet, see if you are able to answer the following questions.

1. How does 'a' effect the equation? How does it change the ellipse?
   
   
   Interactive popup. Assistance may be required.

   Check Your Answer

   As the value of 'a' changes, so does the number beneath the term in the equation. The value of 'a' determines the length of the ellipse along the major axis—in this case, the x-axis.
2. How does 'b' effect the equation? How does it change the ellipse?
   
   
   Interactive popup. Assistance may be required.

   Check Your Answer

   As the value of 'b' changes, so does the number beneath the term in the equation. The value of 'b' determines the length of the ellipse along the minor axis—in this case, the y-axis.
3. What is the relationship between 'a' and 'b' and the x and y intercepts of this particular ellipse?
   
   
   Interactive popup. Assistance may be required.

   Check Your Answer

   The values of 'a' and 'b', correspond to the values of the x- and y-intercepts of this ellipse, respectively. The x-intercepts are (4, 0) and (-4, 0) with the value of a = 4 and the y-intercepts are (0, 3) and (0, -3) with the value of b = 3.