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

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

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.

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?

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.

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?

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

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

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

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

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

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

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)

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

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