2. Circles
4.1
(Chapter 10)

3. Definitions
Circle – the set of all points in a plane that are equidistant from a given point, called the center
Radius – any segment with endpoints at the center and a point on the circle

4. Equations of Circles

5. Example 1: Write an Equation of a Circle Given the Center and the Length of the Radius
Write the equation of a circle, in standard form, with the center at (2, –5) and a radius 7 units long.
Standard Form:
Equation:
You Try:
Center: (–1, 0)
Radius:

6. Example 2 Write an Equation from a Graph
Write an equation of the graph.
1. Find the radius by plugging both
given points into the standard form equation. .
2. Now substitute the coordinates of the center and the radius into the standard form equation.

7. Example 2A
Write an equation for the graph. #1: #2:

8. Example 3: Write an Equation Given the Diameter
Write an equation for a circle if the endpoints of the diameter are at (7, 6) and (–1, –8).
Step 1: Find the center
Center is the midpoint of the diameter
Step 2: Find the radius
The radius is the distance from the center to any point on the circle.
Equation of Circle:

9. Example 4: Graph an Equation in Standard Form
Find the center and radius of the circle. Then graph the circle.
Center:
Radius:
Graph:

10. Example 5: Graph an Equation Not in Standard Form
Find the center and radius of the circle with the equation
Then graph the circle.
Use Completing the Square on both the x and y.

11. Example 5A
Find the center and radius of the circle with the equation Then graph the circle.