2. 1.5 – Circles (Lesson Objectives) Write the standard form of the equation of a circle. Graph a circle by hand and with a calculator using the standard form of the equation of a circle. Work with the general form of an equation of a circle.

3. Definition A Circle is a set of points in the xy plane that are a fixed distance r from a fixed point (h,k), where (h,k) is the center of the circle and r is the radius.

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

5. Every binomial squared has been multiplied out. Every term is on the left side, set equal to 0. General Form of a Circle

6. EX 1 Write the standard form for the equation of a circle with center (3, -2) and a radius of 4.

7. EX 2 Write an equation of a circle with center (-4, 0) and a diameter of 10.

8. EX 3 Write an equation of a circle with center (2, -9) and a radius of.

9. EX 4 Find the coordinates of the center and the measure of the radius.

10. The center is The radius is The equation is 5. Find the center, radius, & equation of the circle. (0, 0) 12 x 2 + y 2 = 144

11. The center is The radius is The equation is 6. Find the center, radius, & equation of the circle. (1, -3) 7 (x – 1) 2 + (y + 3) 2 = 49

12. 7. Graph the circle, identify the center & radius. (x – 3) 2 + (y – 2) 2 = 9 Center (3, 2) Radius of 3

13. Converting from General Form to Standard 1.Move the x terms together and the y terms together. 2.Move C to the other side. 3.Complete the square (as needed) for x. 4.Complete the square(as needed) for y. 5.Factor the left & simplify the right.

14. 8. Write the standard equation of the circle. State the center & radius. Center: (4, 0) radius: 3

15. 9. Write the standard equation of the circle. State the center & radius. Center: (-2, 3) radius: 4

16. 10. Write the standard equation of the circle. State the center & radius.

17. 11. Write the general form of the equation of the circle.

18. Homework 1.5 - p.49 1-4, 7-43 by 4’s, 45 Bring in textbook on Monday Bring in your Notecard for Tuesday’s Ch.1 Test