# 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.**