Then/Now You wrote equations of lines using information about their graphs. Write the equation of a circle. Graph a circle on the coordinate plane.

Concept

Example 1 Write an Equation Using the Center and Radius A. Write the equation of the circle with a center at (3, –3) and a radius of 6. (x – h) 2 + (y – k) 2 = r 2 Equation of circle (x – 3) 2 + (y – (–3)) 2 =6 2 Substitution (x – 3) 2 + (y + 3) 2 = 36Simplify. Answer: (x – 3) 2 + (y + 3) 2 = 36

Example 1 Write an Equation Using the Center and Radius B. Write the equation of the circle graphed to the right. (x – h) 2 + (y – k) 2 = r 2 Equation of circle (x – 1) 2 + (y – 3) 2 =2 2 Substitution (x – 1) 2 + (y – 3) 2 = 4Simplify. Answer: (x – 1) 2 + (y – 3) 2 = 4 The center is at (1, 3) and the radius is 2.

Example 1 A.(x – 2) 2 + (y + 4) 2 = 4 B.(x + 2) 2 + (y – 4) 2 = 4 C.(x – 2) 2 + (y + 4) 2 = 16 D.(x + 2) 2 + (y – 4) 2 = 16 A. Write the equation of the circle with a center at (2, –4) and a radius of 4.

Example 2 Write an Equation Using the Center and a Point Write the equation of the circle that has its center at (–3, –2) and passes through (1, –2). Step 1Find the distance between the points to determine the radius. Distance Formula (x 1, y 1 ) = (–3, –2) and (x 2, y 2 ) = (1, –2) Simplify.

Example 2 Write an Equation Using the Center and a Point Step 2Write the equation using h = –3, k = –2, and r = 4. (x – h) 2 + (y – k) 2 = r 2 Equation of circle (x – (–3)) 2 + (y – (–2)) 2 =4 2 Substitution (x + 3) 2 + (y + 2) 2 = 16Simplify. Answer: (x + 3) 2 + (y + 2) 2 = 16

Example 5 Find the points of intersection between x 2 + y 2 = 16 and y = –x. A.(2, –2) B.(2, 2) C.(–2, –2), (2, 2) D.(–2, 2), (2, –2)