1. Lesson Plan for
Equation of a Circle
Standard: MACC.912.G-GPE.1.1

2. 1) Find the distance between the points (2, 4) & (5, 2)
Bellwork
1) Find the distance between the points (2, 4) & (5, 2)
Find the distance of each segment.
a) b)
3) Solve for r.
a) b) r r y 4 6 x

3. Getting Ready:
The owner of an outdoor adventure course want a way to communicate to all points on the course. They are considering purchasing a walkie-talkie with a range of ½ mile. A model of the course is at the right. Each grid unit represents 1/8 mi. The base station is at (2,4). Do you think the owners should buy the walkie-talkie? Why?
Write down your group’s answer on the whiteboard.

4. 2) How can you express the range of a walkie-talkie?
Getting Ready:
The owner of an outdoor adventure course want a way to communicate to all points on the course. They are considering purchasing a walkie-talkie with a range of ½ mile. A model of the course is at the right. Each grid unit represents 1/8 mi. The base station is at (2,4). Do you think the owners should buy the walkie-talkie? Why?
1) What are the center and the radius of a circle that represent the communication range of a walkie-talkie from the base station?
2) How can you express the range of a walkie-talkie?

5. Lesson Objectives:
1) Find the equation of a circle, given its center and radius.
2) Find the center and the radius of a circle, given its equations.

6. Find the equation of a circle, given its center and radius.
a) What is a circle?
b) How do you find the equation of a circle?

7. Example: Find the equation of a circle with the given radius

8. Finding the equation of a circle with the given center and the radius
Ex. Find the equation of a circle with the center at (8, -1 ) and radius equal to 12

9. Example: Find the equation of a circle with the given center and the radius
Center (3, 5) ; radius = 5
Center (2, -3) ; radius = 4
Center (0, 0); radius = ½

10. 2) Find the equation of a circle, given its center and radius.

11. Write the equation of the circle, given the center and the radius:
a) Center (3, 2), radius = 5 units
(x - h)2 + (y - k)2 = r2
(x - 3)2 + (y - 2)2 = 25
____
b) Center (-5 , 3), radius = √10 unit
___
c) Center (3 , -1), radius = 2√5
d) Center (-3 , -9), radius = 3√7 5
(3, 2)
(x + 5)2 + (y - 3)2 = 10
(x - 3)2 + (y + 1)2 = 20
(x + 3)2 + (y + 9)2 = 63

12. Write the equation of the circle, given the center and a point on the circle:
a) Find the equation of the circle with
center (1, -3), that passes through
the point (2, 2).
(x - h)2 + (y - k)2 = r2
(h = 1), (k = -3)
(x - 1)2 + (y + 3)2 = 26

13. Write the equation of the circle, given the center and a point on the circle:
Find the equation of the circle with the given Center that passes through the given point .
1) Center (3, 5), point (-2, 3)
2) Center (4 , 3), point (0, 0)
3) Center (0 , 0), point (-5, 4)

14. Find the center and the radius of the circle, given its equation.
1) (x – 5)2 + (y + 3)2 = 25
2) (x - 9)2 + (y - 1)2 = 20
3) (x)2 + (y - 3)2 = 10

15. Exit Slip
Do the following:
1) Find the equation of a circle with center (0, 0), and radius = 5
2) Find the equation of a circle with center (3, -2), and radius = 4
3) Find the center and the radius of the circle whose equation is (x + 1)2 + (y - 4)2 = 36