1. Algebra 2 Conic Sections: Circles and Parabolas

2. Circles I can learn the relationship between the center and radius of a circle and the equation of a circle. I can graph circles I can write equations of circles

3. 3 What is a circle? The set of all points equidistant from a given point. That given point: center That distance: radius Other terms: diameter, circumference, area 3

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

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

6. 6 Determine the center and the radius of the following circles: 1. x 2 + (y - 2) 2 = 25 2. (y + 3) 2 + (x - 5) 2 = 10

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

8. Graph the previous circle

9. 9-2 Circles What will the equation of a circle look like if the center is at the origin?

10. Circles Check out this website to see how the equation affects the position of a circle: http://www.shodor.org/interactivate/activities /ConicFlyer/?version=1.6.0_13&browser=M ozilla&vendor=Sun_Microsystems_Inc. http://www.shodor.org/interactivate/activities /ConicFlyer/?version=1.6.0_13&browser=M ozilla&vendor=Sun_Microsystems_Inc.

11. Given: x 2 + y 2 = 16 1. Write an equation of a circle that is translated up 2 units. 2. Write an equation of a circle that is translated down 3 units and right 4. 3. Write an equation of a circle that is translated left 5 units, then reflected over the y-axis!

12. 12 Tangent to a Circle a line that intersects a circle at one point. Can you write and equation of a circle that has a center of (5, -1) and is tangent to the line x = 8? 12

13. 13 Exit Slip Time! Homework: Day 1 on the assignment guide 13