Circles & Ellipses

 

Lesson # 5

Topic: Comparing Circles and Ellipses – Approximate time – 50 minutes

Strategy Used: Compare and Contrast

Objective:

Main AKS:

Differentiation types used in this lesson:

 

Materials Needed: graphing calculators, Ellipse Worksheet, Circle/Ellipse Table

Lesson Procedure:

    1. The teacher should recap the previous lesson, focusing on the general equation for circles that the students discovered.
    2. Have the students graph the equation in their calculators. ( Remind the students to set the calculators to have a square window and have the x:y ratio equal to 1:1.516.) Discuss the main attributes of the ellipse that was graphed:

      3. Center ( 0, 0)

      x-axis of length 3 – major axis

      y-axis of length 2 – minor axis

    3. Working with the same partner as yesterday, have the students work on Ellipse Worksheet. This portion of the activity should take about

      4. 25 – 30 minutes.

    4. Bring the students together and have them volunteer their general equations. After some discussion, make sure every student has a correct general equation for an ellipse written down:

      5. , with center (h, k) and major/minor axes

      of lengths a & b.

    5. Discuss the similarities between circles and ellipses and have them enter their findings on the Venn diagram on the Ellipse Worksheet.

Assessment: Have the students write how circles are a special type of ellipse. Include the general equations for both the circle and the ellipse. Also, include how the radius corresponds to the major and minor axes.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

H/G Algebra 2 Name:__________________________

Ellipse Worksheet

 

Complete this worksheet working with a partner. One of you should be Student A, and one should be Student B.

I.

  1. Graph the following equations in your calculator:

    2. Student A : Student B:

    How are these two graphs similar and how are they different?

    ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

     

  2. Fill in the table with the info for the two graphs. What is the standard equation for each of these ellipses? ** How does the standard equation compare to its graphing equations? Remember that the standard equation is ONE equation, not two separate equations.

II.

  1. Graph the following equations in your calculator:

Student A: Student B:

Compare the two graphs. Fill in the table with the correct information about the two graphs.

III.

Without graphing, predict the graph of:

and .

________________________________________________________________________________________________________________________________________________________________________________________________

Now, graph the equations in your calculator. Were your predictions correct? If not, describe the graph. Enter the appropriate information into the table.

________________________________________________________________________________________________________________________________________________________________________________________________

IV. Predict the standard equations for each of the graphs. Also, create a general equation for ellipses. Be sure we can quickly determine the center and the major/minor axes for each ellipse.

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Name:________________________________________ Date:___________

Circle/Ellipse Table

Standard Equation

Graphing Equations

Center

Radius/Radii