1. 1. Factor 2. Factor 3.What would the value of c that makes a perfect square. Then write as a perfect square. M3U8D3 Warm Up (x+4) 2 (x-7) 2 c = 36 (x+6) 2 NEW SEATS!!!

2. HW Check:

4. M3U8D3 Equations of Circles OBJ: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. G-GPE.1

5. Draw a circle on the coordinate plane with a center at (0, 0) and put a right triangle in it using a point (h, k). Then use the Pythagorean Theorem to get equation of circle. The equation of a circle with center (h,k) and radius r is (x-h) 2 + (y-k) 2 = r 2.

6. [x – (–8)] 2 + (y – 0) 2 = ( 5 ) 2 Substitute (–8, 0) for (h, k) and 5 for r. EXAMPLE 1: Write the standard equation of a circle with center (–8, 0) and radius 5. (x – h) 2 + (y – k) 2 = r 2 Standard form (x + 8) 2 + y 2 = 5Simplify.

7. You try these on your handout: REMEMBER…The equation of a circle with center (h,k) and radius r is (x-h) 2 + (y-k) 2 = r 2.

8. r = (x – h) 2 + (y – k) 2 Use the Distance Formula to find r. = (–15 – 5) 2 + (–13 – 8) 2 Substitute (5, 8) for (h, k) and (–15, –13) for (x, y). Example 2: Write the standard equation of a circle with center (5, 8) that passes through the point (–15, –13). First find the radius. = (–20) 2 + (–21) 2 Simplify. = 400 + 441 = 841 = 29 Then find the standard equation of the circle with center (5, 8) and radius 29. (x – h) 2 + (y – k) 2 = r 2 Standard form (x – 5) 2 + (y – 8) 2 = 29 2 Substitute (5, 8) for (h, k) and 29 for r. (x – 5) 2 + (y – 8) 2 = 841Simplify.

9. Example 3: Find the center and radius of the circle with equation (x + 4) 2 + (y – 1) 2 = 25. Then graph the circle. (x + 4) 2 + (y – 1) 2 = 25 (x – (– 4)) 2 + (y – 1) 2 = 5 2 Relate the equation to the standard form (x – h) 2 + (y – k) 2 = r 2. h k r The center is (– 4, 1) and the radius is 5.

10. You try these on your handout: Completing the square is like the warm up!

11. You try these on your handout: DIVIDE BY 3!

12. Classwork M3U8D2 Equations of Circles Guided Practice Homework M3U8D2 Equations of Circles WS U7 Test Corrections due FRIDAY 12/4/15