1. Changing Forms of Circles

2. Standard Form of a Circle
Center is at (h, k)
r is the radius of the circle

3. General Form of a Circle

4. General Form of a Circle
Every binomial squared has been multiplied out.
Every term is on the left side, equal to 0.
Squared terms go first in alpha order.

5. Completing the Square ax2 + bx + c = 0
Is another way to solve a quadratic equation.
ax2 + bx + c = 0
a needs to be 1.
c needs to be moved to the other side of the = sign

6. Steps to Completing the Square
1. Move the constant to the other side.
2. Add to BOTH sides of the eqn.
3. Factor!

7. Example 1:

8. Example 2:

9. Example 3:

10. Converting from General to Standard
A needs to be 1. Divide if needed.
Move the x terms together and the y terms together.
Move E to the other side of the equals sign.
Complete the square (as needed) for x.
Complete the square(as needed) for y.
Factor the left & simplify the right.

11. 1. Write the standard equation of the circle. State the center & radius.

12. 2. Write the standard equation of the circle. State the center & radius.

13. 3. Write the standard equation of the circle. State the center & radius.

14. 14. Write the general form of the equation of the circle.

15. Homework
Practice WS