# Equation of a Circle Investigation

- Author:
- Lydia Pernia, Mr. Krebs

## Q1. Move the center of circle A to the origin (0,0) and change the radius to 1. This is called the parent function of a circle.

What is the equation of this circle?

## Q2. Leave the center of circle A to the origin (0,0) and change the radius to 3.

What is the equation of this circle?

## Q3. Leave the center of circle A to the origin (0,0) and change the radius to 5.

What is the equation of this circle?

## Q4. Leave the center of circle A to the origin (0,0) and change the radius to 4.

What is the equation of this circle?

## Q5. Examine the equations above.

What happens to the radius in the equation? Change the radius a few times more to verify your answer.

## Q6. Move the center of the circle to ( 6, 0) and change the radius to 3.

What is the new circle equation?

## Q7. Move the center of the circle to ( -2, 0) and leave the radius to 3.

What is the new circle equation?

## Q8. Examine the equations above.

What happened to the equation when the x coordinate of the center is positive? How about when it is negative?

## Q9. Move the center of the circle to ( 0, 3) and leave the radius to 3. Write the equation. Then move the center of the circle to ( 0, -5) and leave the radius to 3.

What are the two new equations?

## Q10. Examine the equations.

What happened to the equation when the y coordinate of the center is positive? How about when it is negative?

## Q11. The general equation for a circle is ( x - h )^2 + ( y - k )^2 = r^2, where ( h, k ) is the center and r is the radius.

Write the equation of a circle with a center at ( -3, 4) and a radius of 8.