Objective: To write an equation of a circle. 11.5 Equations of Circles Objective: To write an equation of a circle.

Equation of a Circle The center of a circle is given by (h, k) The radius of a circle is given by r The equation of a circle in standard form is (x – h)2 + (y – k)2 = r2

Ex. 1: Writing a Standard Equation of a Circle Write the standard equation of the circle with a center at (-4, 0) and radius 7.1 (x – h)2 + (y – k)2 = r2 Standard equation of a circle. Substitute values. [(x – (-4)]2 + (y – 0)2 = 7.12 Simplify. (x + 4)2 + (y – 0)2 = 50.41

Example 2:Writing Equations of Circles Write the standard equation of the circle: Center (-3, 8) Radius of 6.2 (x + 3)2 + (y – 8)2 = 38.44 (x – h)2 + (y – k)2 = r2 [(x – (-3)]2 + (y – 8)2 = 6.22

Example 3: Writing Equations of Circles Write the standard equation of the circle: Center (0, 6) Radius of x 2 + (y – 6)2 = 7 (x – h)2 + (y – k)2 = r2 [(x – 0]2 + (y – 6)2 = (√7)2

Example 4: Writing Equations of Circles Write the standard equation of the circle: Center (-1.9, 8.7) Radius of 3 (x + 1.9)2 + (y – 8.7)2 = 9 (x – h)2 + (y – k)2 = r2 [(x – (-1.9)]2 + (y – 8.7)2 = 32

Ex. 5: Writing a Standard Equation of a Circle The point (1, 2) is on a circle whose center is (5, -1). Write a standard equation of the circle. r = Use the Distance Formula r = Substitute values. r = Simplify. r = Simplify. r = Addition Property Square root the result. r = 5

Ex. 5 (cont.): Writing a Standard Equation of a Circle The point (1, 2) is on a circle whose center is (5, -1). Write a standard equation of the circle. (x – h)2 + (y – k)2 = r2 Standard equation of a circle. Substitute values. [(x – 5)]2 + [y –(-1)]2 = 52 Simplify. (x - 5)2 + (y + 1)2 = 25

Ex. 6: Writing a Standard Equation of a Circle The point (-1,-4) is on a circle whose center is (-4, 0). Write a standard equation of the circle. r = Use the Distance Formula Substitute values. r = r = Simplify. r = Simplify. r = Addition Property Square root the result. r = 5

Ex. 6 (cont.): Writing a Standard Equation of a Circle The point (-1, -4) is on a circle whose center is (-4, 0). Write a standard equation of the circle. (x – h)2 + (y – k)2 = r2 Standard equation of a circle. Substitute values. [(x – (-1))]2 + [y –(-4)]2 = 52 Simplify. (x - 1)2 + (y + 4)2 = 25

Example 7: Give the center and radius of the following circles: A. B. Center: ( 4, 3 ) ; Radius: 4 Center: ( 0, -7 ) ; Radius: 1

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