Worksheet for Lesson on Ellipses

 

Graph the following problems:  Determine the effect of changing (h,k) and the values of and  for the ellipse.  Record the location of the foci and the length of the latus rectum for each problem.

 

1.                                                 4. 

 

2.                                5. 

 

3.                                6. 

 

Conclusions about (h,k):______________________________________

 

Conclusions about and :___________________________________

 

 

Based on your observations write the equations for the following ellipses.

 

1.                  (h.k) = (3, -2) and a=5, b=2 and major axis horizontal

2.                  (h.k) = (3, -2) and a=5, b=2 and major axis vertical

3.                  (h,k) = (-1,-3) and a=5, c=4 and major axis horizontal

4.                  (h,k) = (-1,-3) and b=3, c=4 and major axis vertical

 

Use the computer program to graph the following circles and record your observations concerning (h,k) and the radius.  Suppose you wanted to find the diameter of each circle.  What would you do?

 

1.                                     2. 

 

3.                    4. 

 

To find the diameter when given the radius, I_______________________

 

To find the radius when given the diameter, I_______________________

 

 

 

  1. Write and explanation of the effects of changing (h,k) on both the circle and the ellipse.
  2. Explain the effect of  and  on the ellipse.
  3. Create 5 problems of your own that would be ellipses and circles.
  4. Give 5 sets of data that would be sufficient for a partner to write the equation of the circle or the ellipse.  For one of the circles, give the diameter instead of the radius.
  5. List the problems and have your partner solve them, using the computer graphing program.
  6. Write a summary of the difficulties, if any, that you and your partner experienced when checking your problems.  If no problems were encountered, sketch the graphs of the problems and show the equations.

 

Simplify, predict what the ellipse or circle will look like and then using graphing calculator to confirm your findings for the following problems:

 

1.                               3.                   5.                        

 

2.                               4. 

 

Click here for graphs of these equations

 

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