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_______________________
- Write and explanation of the effects
of changing (h,k) on both the circle and the ellipse.
- Explain the effect of and on the ellipse.
- Create 5 problems of your own that
would be ellipses and circles.
- 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.
- List the problems and have your
partner solve them, using the computer graphing program.
- 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