Sullivan Algebra and Trigonometry: Section 2.4 Circles Objectives Write the Standard Form of the Equation of a Circle Graph a Circle Find the Center and Radius of a Circle and Graph It

Definition: A circle is a set of points in the xy-plane that are a fixed distance r from a fixed point (h, k). The fixed distance r is called the radius, and the fixed point (h, k) is called the center of the circle. x y (h, k) r (x, y)

Definition: The standard form of an equation of a circle with radius r and center (h, k) is

Graph ()()xy 

Step 1: Plot the center of the circle. y x (-1,3) Step 2: Plot points above, below, left, and right of the center by traveling a distance equal to the radius. (-1, 7) (3,3) (-1, -1) (-5, 3) Step 3: Graph the circle.

The general form of the equation of a circle is: To find the center, radius, and graph of a circle in general form, first rewrite the equation of the circle in standard form using the process of completing the square.

Find the center and radius of Center: (2,-4) Radius: 5