1. 11.3 – Writing and Graphing Circles
Secondary Math 2
11.3 – Writing and Graphing Circles

2. Warm-Up:
Solve for the ‘?’

3. Turn in 11.1 Questions on 11.2

5. What You Will Learn
I will be able to create an equation for and graph any circle.

6. What’s the purpose of circles?
Telecommunications
Doppler Effect
Water droplets

7. Pythagorean theorem and the circle equationx y
𝑎 2 + 𝑏 2 = 𝑐 2
𝑥 2 + 𝑦 2 = 𝑟 2

8. Equation of a circle
𝑥−ℎ 𝑦−𝑘 2 = 𝑟 2
Center = (𝒉, 𝒌)

9. Identify the center and radius
𝑥− 𝑦−9 2 =121
Center:
Radius:
𝑥− 𝑦−1 2 =49
𝑥 𝑦−1 2 =36
Center:
Radius:
𝑥 2 + 𝑦+2 2 =13

10. Sketch the graph from an equation
Identify Center
Plot center on graph
Identify Radius
Graph radius in 4 directions (N, S, E, W)
Draw Circle
Connect the dots in a circular shape
𝑥− 𝑦−2 2 =9

11. 𝑥+6 2 + 𝑦 2 =4 Identify Center Identify Radius Draw Circle
Plot center on graph
Identify Radius
Graph radius in 4 directions (N, S, E, W)
Draw Circle
Connect the dots in a circular shape
𝑥 𝑦 2 =4

12. Writing the equation 𝑥−ℎ 2 + 𝑦−𝑘 2 = 𝑟 2
Center: 10, 12 ; Radius: 5
Center: 4, 6 ; Radius: 12
Center: −4, 2 ; Radius: 6
Center: (−1, −5); Radius: 11

13. Write the equation: Center; “Passes through point”
Plug center in for (h, k)
Plug “Passes through point” in for (x, y)
Solve for the radius.
𝑥−ℎ 𝑦−𝑘 2 = 𝑟 2
Example:
Center (5, -2)
Passes through Point (4, 0)

14. Finding the Equation of the circleʘ𝐴
Find the Center; (h, k)
Find the Radius; r
Write the Equation (Plug it in)
𝑥−ℎ 𝑦−𝑘 2 = 𝑟 2

15. Finding the Equation of the circleʘ𝐵
Find the Center; (h, k)
Find the Radius; r
Write the Equation (Plug it in)
𝑥−ℎ 𝑦−𝑘 2 = 𝑟 2

16. Finding the Equation of the circleʘ𝑂
Find the Center; (h, k)
Find the Radius; r
Write the Equation (Plug it in)
𝑥−ℎ 𝑦−𝑘 2 = 𝑟 2