Chapter 12: Circles

1
Chapter 12 Circles

• 12.5
• Circles in the Coordinate Plane

2
Conic Sections

• These are cross sections of a cone

3
Theorem 12-13

• An equation of a circle with center (h,k) and
  radius r is

This is called the Standard Form of an Equation
of a Circle.
4
Example 1

• Write the standard equation of a circle with
  center (5,-2) and radius 7.

5
Example 2

• Write the standard equation of a circle with
  center (1,-3) that passes through the point (2,2).

6
Example 2a

• Write the standard equation of the circle with
  center (2,3) that passes through the point (-1,1).

7
Example 3

• Find the center and radius of the circle with
  equation (x 7)2 (y 2)2 64. Then graph
  the circle.

8
Example 3a

• Find the center and radius of the circle with the
  equation (x 2)2 (y 3)2 100. Then graph
  the circle.

9
Example 3b

• Find the center and radius of the circle with
  equation (x 4)2 (y 1)2 25. Then graph
  the circle.

10
Challenge

• The point (-1,4) is on a circle with center
  (5,-2). Find the standard equation and diameter
  of the circle. Leave your answer in simplest
  radical form.

11
Homework

• P. 697
• 2 20 even, 28 38 even