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Circle equation

Note:  If r2 is not a perfect square then leave r in simplified radical form but use the decimal equivalent for graphing.  Example:

 

1) Graph the following circle:  

 

  1. (x - 3)2 + (y + 1)2 = 4
  2.  (x – 2)2 + (y – 5)2 = 9
  3.  (y + 4)2 + (x + 2)2 = 16

 

    
 
  
 

 

 

 

 

 

 

 

 

 

 

 

 

2) For each circle: Identify its center and radius.

 

a. (x + 3)2 + (y – 1)2 = 4

 

 

Center:_____________

 

Radius:_____________

b. x2 + (y – 3)2 = 18

 

 

Center:___________

 

Radius:____________  

c. (y + 8)2 + (x + 2)2 = 72

 

 

Center:_____________

 

Radius:_____________

 

 

3) Write the equation of the following circles:

 

                                                                                               

 

 

 

 

 

 

 

 

 

 

4) Give the equation of the circle that is tangent to the y-axis and center is (-3, 2).        

                                                                                               

                                                                       

 

 

 

                       

 

 

 

 

 

Putting Equations in Standard Form

Example 1:  x2 + y2 + 6x – 8y – 11 = 0                                   Example 2: x2 + y2 – 2x +  6y – 10 = 0

(x2 + 6x) + (y2 – 8y) = 11

(x2 + 6x + 9) + (y2 – 8y + 16) = 11 + 9 + 16             

(x + 3)2  + (y – 4)2 = 36

Center: (-3, 4)   Radius:  6                                                      Center:_______ Radius:__________

 

6) Find the standard form, center, and radius of the following circles:

 

6a) x2 + y2 – 4x + 8y – 5 = 0

 

 

            Center:___________

Radius:______________

6b) 4x2 + 4y2 + 36y + 5 = 0

 

 

 

 

 

 

Center:________

Radius:___________

 

 

7) Graph the following circles:

 

7a) x2 – 2x + y2 + 8y – 8 = 0

7b) x2 + y2 – 6x + 4y – 3 = 0          

 

 

 

 

    
 
  
 

 

 

 

 

 

 

 

 

 

 

 

 

 


 

8) Give the equation of the circle whose center is (5,-3) and goes through (2,5)                        

 

9) Give the equation whose endpoints of a diameter at (-4,1) and (4, -5)

 

 

 

 

 

 

 

 

10) Give the equation of the circle whose center is (4,-3) and goes through (1,5)                      

 

11) Give the equation whose endpoints of a diameter at (-3,2) and (1, -5)

 

 


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