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Chapter 12: Circles

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Chapter 12: Circles 12.5 Circles in the Coordinate Plane Example 3b Find the center and radius of the circle with equation (x + 4)2 + (y 1)2 = 25. – PowerPoint PPT presentation

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Title: 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
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