Objectives Write equations and graph circles in the coordinate plane.

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.

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.

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.

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.

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

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).

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).