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The equation of a circle is given as 2x^2 + 2y^2 + 4x + 12y + 6 = 0. What are the center, C, and the radius, r of the circle?

 Aug 10, 2021
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2x^2 + 2y^2 + 4x + 12y + 6 = 0    divide thru by 2

x^2  + 2x       + y^2 + 6y   =    -6      complete the square for x and y

(x+1)^2         +  (y+3)^2    = - 6  +1 + 9

(x+1)^2         +  (y+2)^2    =   4                        

 

this is a circle equation of the form     (x-h)^2   + (y-k)^2   = r ^2        center = (h,k) = ( -1,-2)    radius = 2

 Aug 10, 2021

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