Circle Shifts

Author:
Annie
Topic:
Circle

Directions

1. Use the sliders to explore the parameters involved in determining the equation of a circle. 2. Answer the questions below.

Question 1

Describe the role of "r" in the equation of a circle.

Question 2

Describe the role of "h" in the equation of a circle.

Question 3

Describe the role of "k" in the equation of a circle.

Question 4

Set r = 5, C to (0,0) and A to (3,4). What do you notice about the right triangle associated with the radius and its vertical and horizontal components? Once you have found this relationship, find at least 3 other "nice" points on this circle.

Question 5

Find another circle (change the radius and/or the center) and find a set of point that demonstrate the relationship you determined above.

Question 6

What is the equation of "Match My Function #1"?

Check all that apply

Question 7

What is the equation of "Match My Function #2"?

Check all that apply

Equation Formats

There are a number of ways to write the equation of a circle. For example: can also be written: to reflect that a circle is just a special ellipse. It can also be written: Work with your group to make sure you understand how one might convert between these 3 forms of the equation before attempting the next set of questions.

Question 8

What is the radius of the circle described by the equation ?

Check all that apply

Question 9

What is the radius of the circle described by the equation ?

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Question 10

What is the center of the circle described by the equation ?

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Question 11

What is the radius of the circle described by the equation ?

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