1. Algebra 2 Chapter 9 Conic Sections: Circles and Parabolas

2. 9-2 Circles WARMUP: Give the constant that makes each of the following a perfect square trinomial: 1. x 2 + 8x + ____ 2. y 2 – 24x + ____ 3. x 2 – x + ____ 4. y 2 + 3y + ____

3. 9-2 Circles Objective: To learn the relationship between the center and radius of a circle and the equation of a circle.

4. 9-2 Circles As we saw previously, the term Conics comes from slices of a double cone creating certain shapes. The simplest of these is the circle: Circle: the set of all points in a plane that are a fixed distance, the radius, from a fixed point, the center.

5. 9-2 Circles C(5,1) P(x,y) Start with the distance formula: Every circle has an equation of this form.

6. 9-2 Circles Equation of a circle: The circle with center ( h, k ) and radius r has the equation:

7. 9-2 Circles What is the equation of a circle with center ( -4, 3 ) and radius 5?

8. 9-2 Circles

9. What will the equation of a circle look like if the center is at the origin?

10. 9-2 Circles Check out this website to see how the equation affects the position of a circle: http://www.shodor.org/interactivate/activities/Co nicFlyer/?version=1.6.0_13&browser=Mozill a&vendor=Sun_Microsystems_Inc.

11. 9-2 Circles Typical test problem: Find the center and radius of the following equation of a circle:

12. 9-2 Circles Problems like the homework:

13. 9-2 Circles Homework:

14. 9-2 Circles