Download Chapter 12: Circles

Chapter 12: Circles
12.5
Circles in the Coordinate Plane
Conic Sections
• These are cross sections of a cone:
Theorem 12-13
• An equation of a circle with center (h,k) and radius r
is:
x  h    y  k 
2
2
r
2
This is called the Standard Form of an Equation of a Circle.
Example 1
• Write the standard equation of a circle with center
(5,-2) and radius 7.
Example 2
• Write the standard equation of a circle with center
(1,-3) that passes through the point (2,2).
Example 2a
• Write the standard equation of the circle with
center (2,3) that passes through the point (-1,1).
Example 3
• Find the center and radius of the circle with
equation (x – 7)2 + (y + 2)2 = 64. Then graph the
circle.
Example 3a
• Find the center and radius of the circle with the
equation (x – 2)2 + (y – 3)2 = 100. Then graph the
circle.
Example 3b
• Find the center and radius of the circle with
equation (x + 4)2 + (y – 1)2 = 25. Then graph the
circle.
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.
Homework
• P. 697
• 2 – 20 even, 28 – 38 even