This document provides instruction on writing equations of circles. It begins by defining a circle as all points in the xy-plane that are a fixed distance r from a central point (h,k), known as the radius. The standard form of a circle equation is presented as (x-h)2 + (y-k)2 = r2, where (h,k) are the coordinates of the center and r is the radius. Examples are given of writing circle equations in standard form given the center and radius. Converting a circle equation from general to standard form is also demonstrated through completing the square. Homework problems are assigned from the text.

2. 1.5 – Circles (Lesson Objectives)
• Write the standard form of the
equation of a circle.
• Graph a circle by hand and with a
calculator using the standard form of
the equation of a circle.
• Work with the general form of an
equation of a circle.

3. Definition
A Circle is a set of
points in the xy
plane that are a
fixed distance r from
a fixed point (h,k),
where (h,k) is the
center of the circle
and r is the radius.

4. Standard Form of a Circle
Center is at (h, k)
   
2 2 2
x h y k r
   
r is the radius of the circle

5. Every binomial squared has been
multiplied out.
Every term is on the left side, set
equal to 0.
2 2
: 4 6 3 0
    
Example x y x y
General Form of a Circle

6. EX 1 Write the standard form for the equation of a
circle with center (3, -2) and a radius of 4.
   
2 2 2
+
x h y k r
  
   
 
2
2 2
3 + 2 4
x y
   
   
2 2
3 + 2 16
x y
  

7. EX 2 Write an equation of a circle with
center (-4, 0) and a diameter of 10.
   
2 2 2
+
x h y k r
  
 
   
2 2 2
4 + 0 5
x y
   
 
2 2
4 +y 25
x  

8. EX 3 Write an equation of a circle with
center (2, -9) and a radius of .
11
   
 
2
2
2
2 9 11
x y
    
   
2 2 2
+
x h y k r
  
   
2 2
2 + y+9 11
x  

9. EX 4 Find the coordinates of the center and
the measure of the radius.
   
2 2 2
6 + 3 25
x y
  

10. The center is
The radius is
The equation is
5. Find the center, radius, &
equation of the circle.
(0, 0)
12
x2 + y2 = 144

11. The center is
The radius is
The equation is
6. Find the center, radius, &
equation of the circle.
(1, -3)
7
(x – 1)2 + (y + 3)2 = 49

12. 7. Graph the circle, identify
the center & radius.
(x – 3)2 + (y – 2)2 = 9
Center (3, 2)
Radius of 3

13. Converting from General Form to
Standard
1. Move the x terms together and the y
terms together.
2. Move C to the other side.
3. Complete the square (as needed)
for x.
4. Complete the square(as needed) for
y.
5. Factor the left & simplify the right.

14. 2 2
( 8 ) 7
   
x x y
8. Write the standard equation of the circle.
State the center & radius.
2 2
8 7 0
x y x
   
Center: (4, 0) radius: 3
2 2
( 4) 9
x y
  
2 2
( 8 )
16 16
7
     
x x y

15.    
2 2
4 6 3
   
x x y y
9. Write the standard equation of the circle.
State the center & radius.
2 2
4 6 3 0
    
x y x y
Center: (-2, 3) radius: 4
   
2 2
2 3 16
   
x y
   
2 2
4 6 9
3
9
4 4
     
 
x x y y

16.    
2 2
8 2 10
    
x x y y
10. Write the standard equation of the circle.
State the center & radius.
2 2
2 2 16 4 20 0
    
x y x y
   
2 2
4 1 7
   
x y
   
2 2
8 2 1 1
16 16
10

  
    
x x y y
2 2
8 2 10 0
    
x y x y
: (4, 1) : 7 2.6
 
Center Radius

17. 11. Write the general form of the equation of the
circle.
   
2 2
4 3 36
   
x y
2 2
8 16 6 9 36
     
x x y y
2 2
8 16 6 9 36 0
      
x x y y
2 2
8 6 11 0
    
x y x y

18. Homework
• 1.5 - p.49 1-4, 7-43 by
4’s, 45
• Bring in textbook on
Monday
• Bring in your Notecard
for Tuesday’s Ch.1 Test