CIRCLES Unit 3-2

Equations we’ll need: Distance formula Midpoint formula

Definitions Circle: Set of all points in a plane that is a fixed distance from a fixed point Center: The fixed equidistance point of the circle Radius: The fixed equidistance length of the circle

Circle Equation

Example 1 Name the center and the radius of this circle, and graph it

Example 1 Name the center and the radius of this circle, and graph it

Example 2 Write an equation of the circle with its center at (–3, 5), the radius is 5 and graph it.

Example 3 Name the center and the radius of this circle, and graph it

YOUR TURN! Graph the equation

2.3 - Circles105/24/2015 4:02 AM Example 4 Find the radius, graph the circle, and write the equation in standard form with the given center of (2, -3) and the point (1, 0). C radius

2.3 - Circles115/24/2015 4:02 AM Example 4 Find the radius, graph the circle, and write the equation in standard form with the given center of (2, -3) and the point (1, 0). C radius =

2.3 - Circles125/24/2015 4:02 AM Write a circle equation whose center is at the origin and passes through (1, –6). Example 5

2.3 - Circles135/24/2015 4:02 AM Write a circle equation whose center is at (1, 0) and passes through (-2, 3) YOUR TURN!

2.3 - Circles145/24/2015 4:02 AM Write a circle equation whose endpoints of a diameter are (-5, 2) and (3, 6). Example 6 Diameter Center

2.3 - Circles155/24/2015 4:02 AM Write a circle equation whose endpoints of a diameter are (-5, 2) and (3, 6). Example 6 Center Radius

2.3 - Circles165/24/2015 4:02 AM Write a circle equation whose endpoints of a diameter are (-5, 2) and (3, 6). Example 6

2.3 - Circles175/24/2015 4:02 AM YOUR TURN! Write a circle equation whose endpoints of a diameter are (5, 4) and (-1, -6).

2.3 - Circles185/24/2015 4:02 AM Determine the equation of this circle by the graph given Example 7

2.3 - Circles195/24/2015 4:02 AM YOUR TURN! Determine the equation of this circle by the graph given

2.3 - Circles205/24/2015 4:02 AM Assignment WORKSHEET!