1. Objectives
Write equations and graph circles in the coordinate plane.

2. The equation of a circle is based on the Distance Formula and the fact that all points on a circle are equidistant from the center.

4. Example 1A: Writing the Equation of a Circle
Write the equation of each circle.
J with center J (2, 2) and radius 4
(x – h)2 + (y – k)2 = r2
Equation of a circle
Substitute 2 for h, 2 for k, and 4 for r.
(x – 2)2 + (y – 2)2 = 42
(x – 2)2 + (y – 2)2 = 16
Simplify.

5. Example 1B: Writing the Equation of a Circle
Write the equation of each circle.
K that passes through J(6, 4) and has center K(1, –8)
Distance formula.
Simplify.
Substitute 1 for h, –8 for k, and 13 for r.
(x – 1)2 + (y – (–8))2 = 132
(x – 1)2 + (y + 8)2 = 169
Simplify.

6. Example 1C: Writing the Equation of a Circle
Write the equation of each circle.
P with center P(0, –3) and radius 8
(x – h)2 + (y – k)2 = r2
Equation of a circle
Substitute 0 for h, –3 for k, and 8 for r.
(x – 0)2 + (y – (–3))2 = 82
x2 + (y + 3)2 = 64
Simplify.

7. If you are given the equation of a circle, you can graph the circle by identifying its center and radius.

8. Example 2A: Graphing a Circle
Graph x2 + y2 = 16.
Step 1: Find the radius.
Since the radius is , or 4, use ±4.
Step 2: Find the center (h, k)
The center is (0, 0).

9. Example 2B: Graphing a Circle
Graph (x – 3)2 + (y + 4)2 = 9.
Step 1: Find the radius.
= 3
Step 2: Find the center (h, k)
The equation of the given circle can be written as
(x – 3)2 + (y – (– 4))2 = 32.
So h = 3, k = –4, and r = 3.
The center is (3, –4).