Circles 4.1 (Chapter 10)

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

Equations of Circles

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:

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.

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

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:

Example 4: Graph an Equation in Standard Form Find the center and radius of the circle. Then graph the circle. 1. 2. Center: Radius: Graph:

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.

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