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Find the center and radius of a circle with equation x^2+y^2-1/2x+y=1/2

 Dec 16, 2019
 #2
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Rearrange as

 

x^2 - (1/2)x +  y^2 + y  =  1/2      complete the square on x and y

 

x^2 - (1/2)x + 1/16 + y^2 + y + 1/4  =  1/2 + 1/16 + 1/4

 

Factor  and simplify

 

(x - 1/4)^2  + (y + 1/2)^2  =  8/16 + 1/16 + 4/16

 

(x - 1/4)^2  + (y + 1/2)^2  =  13/16

 

Center  = (1/4 , -1/2)

Radius = √ (13/16 )  =  √13  / 4

 

 

cool cool cool

 Dec 16, 2019

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