1. Circles

2. Unit Vocabulary Circle- Set of all points (x, y) equidistant
(radius: r) from fixed point (center).
Tangent Line- A line tangent to a circle, perpendicular to radius at point of tangency.
Completing the Square- method of solving quadratic equations with lead coeff. of 1.
Ex. x2 – 2x + y2 – 2y – 98 = 0

3. Standard Form: Center at the origin: x2 + y2 = r2 Center: (0, 0)
Radius: r
Center translated: (x - h)2 + (y - k)2 = r2
Center: (h, k)

4. Ex. Identify the center and radius.
1. x2 + y2 = 9
2. (x + 7)2 + (y - 5)2 = 100
3. x2 + y2 = 48
4. (x - 6)2 + (y + 3)2 = 64

5. Ex. Write the equation of the circle.
5. Center: Origin, radius: 8
6. Center: (-3, 9), radius: ¾
7. Center: (6, -2), diameter: 24
8. Center: (0, 11), diameter: 8

6. Ex. Graph the following circles.
Plot the center.
Count radius left, right, up down
9. x2 + y2 = (x - 2)2 + (y + 1)2 = 16

7. Rewrite the following equation in center-radius form of the equation of a circle. Identify the center and radius.
11. x2 – 14x + y2 – 8y = -29
12. x2 – 18x + y2 – 16y = -120

8. Rewrite the following equation in center-radius form of the equation of a circle. Identify the center and radius.
x2 – 4x + y2 – 4y – 92 = 0
14. x2 + 6x = -y2 + 8y - 24

9. Real-Life
14. A furniture store advertises free delivery up to a 50 mile radius from the store. If a customer lives 28 miles east and 41 miles north of the store, does the customer qualify for free delivery?

10. Homework
Circles
Worksheet