10.6 Equations of a Circle Standard Equation of a Circle Definition of a Circle

A circle is a set of points a given distance from one point called the center. The distance from the center is called the radius

Standard equation of the circle If the circle is at the origin x 2 + y 2 = r 2 r is the radius If the circle is not at the origin The center is at (h, k)

Standard equation of the circle If the circle is at the origin x 2 + y 2 = r 2 r is the radius If the circle is not at the origin Solve for r

Write the equation of Circle Center at ( -5,0) and radius 4.8 h =? k =? r = 4.8

Write the equation of Circle Center at ( -5,0) and radius 4.8 h =-5 k =0 r = 4.8

Write the equation of Circle Center at ( 4, -3) and a point on the circle (2,1) h = k = r = x = y =

Write the equation of Circle Center at ( 4, -3) and a point on the circle (2,1) h = 4 k = - 3 r = x = 2 y = 1

Write the equation of Circle Center at ( 4, -3) and a point on the circle (2,1) h = 4 k = - 3 r 2 = 20 x = 2 y = 1

Given the equation of the Circle (x – 13) 2 + (y – 6) 2 = 5 2 Tell if the point is inside or outside the circle. (5, 6)

Given the equation of the Circle (x – 13) 2 + (y – 6) 2 = 5 2 Tell if the point is inside or outside the circle. (5, 6)(5 -13) 2 + (6 – 6) 2 is it, or = 5 2 ( - 8) = 64 = 25 Greater then outside the circle. Less then Inside the circle. Equal is on the circle.

Given the equation of the Circle (x – 13) 2 + (y – 6) 2 = 5 2 Tell if the point is inside or outside the circle. (5, 6)Outside (14,8)

Given the equation of the Circle (x – 13) 2 + (y – 6) 2 = 5 2 Tell if the point is inside or outside the circle. (5, 6)Outside (14,8)In (20, 9)

Given the equation of the Circle (x – 13) 2 + (y – 6) 2 = 5 2 Tell if the point is inside or outside the circle. (5, 6)Outside (14,8)In (20, 9)Outside

Given the equation of the Circle (x – 13) 2 + (y – 6) 2 = 5 2 Tell if the point is inside or outside the circle. (5, 6)Outside (14,8)In (20, 9)Outside (16, 2)

Given the equation of the Circle (x – 13) 2 + (y – 6) 2 = 5 2 Tell if the point is inside or outside the circle. (5, 6)Outside (14,8)In (20, 9)Outside (16, 2)On

Homework Page 638 – 639 # 7 – 25,