To Know kinds of Circle Equations, Look For Center and Radius

    THERE ARE 3 TYPES OF CIRCLE EQUATIONS:

1.    The center (0,0) equation : x² + y² = r²     

2.    The center (a, b) equation 1 : (x-a)² + (y-b)² =r²

3.     The center (a, b) equation 2 :  x² + y² + Ax + By + C = 0       atau

                                           x² + y² - 2ax – 2by + a²  + b² - r² = 0     

Description :   -    a,b  =          center of circle

-        x,y =          a point on the circle

-        r     =          radius

-        A    =          - ½ a

-        B    =          - ½ b

-        C =             a²  + b² - r²     

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I.                HOW TO FIND RADIUS AND CENTER 

 if equation of circle is known

Specify the center and radius of the following circle equation:

1.     Center (0,0) equation : x² + y² = r²   example :

·       x² + y² = 100  -->  center (0,0) radius = 10 because100 = r²  not r ^^

·       x² + y² + 19 = 100 -->  center  (0,0) radius = √100-19 = √81 = 9

·        

2.     Center (a,b) equation 1 : (x-a)² + (y-b)² =r² example :

·       (x+3)² + (y+8)² = 6² --> center (3,8) ; r = 6

·       (x+9)² + (y+1)² = 100 --> center (9,1) ; r = 10

3.    Center (a,b) equation 2 :  x² + y² + Ax + By + C = 0 

·       2x² + 2y² - 8x + 5 = 0 

A = 2 -----> - ½ a = -2 ----> a = 4

B = 0 -----> -  ½ b = 0 ----> b = 0

C = a²  + b² - r² 

5 =  (4)²  + 0² - r²     

r² =  16 – 5 = 9 à r = 3

center = (4,0) r = 3

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