EXAMPLE 3 Write the standard equation of a circle The point (–5, 6) is on a circle with center (–1, 3). Write the standard equation of the circle. SOLUTION To write the standard equation, you need to know the values of h, k, and r. To find r, find the distance between the center and the point (–5, 6) on the circle.

EXAMPLE 3 Write the standard equation of a circle r =[–5 – (–1)] 2 + (6 – 3) 2 = (–4) = 5 Standard equation of a circle Simplify. Substitute (h, k) = (–1, 3) and r = 5 into the standard equation of a circle. (x – h) 2 + (y – k) 2 = r 2 [x – (–1)] 2 + (y – 3) 2 = 5 2 (x +1) 2 + (y – 3) 2 = 25 Substitute. Simplify. The standard equation of the circle is (x +1) 2 + (y – 3) 2 = 25. ANSWER

GUIDED PRACTICE for Example 3 3. The point (3, 4) is on a circle whose center is (1, 4). Write the standard equation of the circle. SOLUTION To write the standard equation, you need to know the values of h, k, and r. To find r, find the distance between the center and the point (3, 4) on the circle. r =[(3 – 1)] 2 + (4 – 4) 2 = 2 Simplify. 4 =

GUIDED PRACTICE for Example 3 Standard equation of a circle Substitute (h, k) = (1, 4) and r = 2 into the standard equation of a circle. (x – h) 2 + (y – k) 2 = r 2 [x – (1)] 2 + (y – 4) 2 = 2 2 (x –1) 2 + (y – 4) 2 = 4 Substitute. Simplify. The standard equation of the circle is (x – 1) 2 + (y – 4) 2 = 4. ANSWER

GUIDED PRACTICE for Example 3 4. The point (–1, 2) is on a circle whose center is (2, 6). Write the standard equation of the circle. SOLUTION To write the standard equation, you need to know the values of h, k, and r. To find r, find the distance between the center and the point (–1, 3) on the circle. r =[(– 1– 2)] 2 + (2– 6) 2 = 5 Simplify. (25) =

GUIDED PRACTICE for Example 3 Standard equation of a circle Substitute (h, k) = (2, 6) and r = 5 into the standard equation of a circle. (x – h) 2 + (y – k) 2 = r 2 [x – 2 ] 2 + (y – 6) 2 = 5 2 (x – 2) 2 + (y – 6) 2 = 25 Substitute. Simplify. The standard equation of the circle is (x – 2) 2 + (y – 6) 2 = 25. ANSWER