Part 3

Author:: Sidney Scott

Note that the center of the circle is at the origin (0,0), and the radius is 1. Adjust slider 'h' so that h=2.

Question 1

A. What is the formula for the circle (given in the Conic section to the left of the graph?) B. What is the center of the circle?

Adjust slider 'h' so that h=2.

Question 2

What is different about the formula and the center of the this circle from that of the circle in the question 1? (Hint: what happened to the signs?)

Return slider 'h' to h=0 so the circle is back at the origin. Adjust slider 'k' so that k=3.

Question 3

A. What is the formula for the circle? B. What is the center of the circle?

Adjust slider 'k' so that k=-1.

Question 4

What happened when you made slider 'k' negative? What effect did this change have on the formula and center of the circle?

Manipulate the sliders until you notice a pattern between the values for 'h' and 'k' and the formula for circle c.

Question 5

A. Using variables, what are the general coordinates of the center of the circle? B. Based on the pattern you discovered, what is the general formula for a circle?

On the graph below, plot the following circles (either by manipulating the sliders, dragging the circle, or by creating an entirely new circle using the tool bar). Note their equations below.

Graph A

Center: (2, -3) Radius: 4

Graph B

If h=1, k=5, and r=2, what is the... A. Center: B. Radius: C. Equation:

Graph C

Center: (-5, 4) Radius: (sqrt(3))

Question 6

Do I have to have a graph to be able to answer the above questions about Graphs A, B, and C? Why or why not?

Once you have answered all the questions in Part 3, you may move on to the Post-Assessment on GoFormative.