Hi,

Showing graphically:  

x^2+y^2+2x+2y=0   |completing squares

x^2+2x+ y^2+2y =0 

(x+1)^2 -1 + (y+1)^2 -1 = 0

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



x^2+y^2+4x+6y+12=0  |completing squares

x^2+4x + y^2+6y +12=0

(x+2)^2 -4 + (y+3)^2 -9 + 12 = 0

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

Algebraically:

 x^2+y^2+2x+2y = x^2+y^2+4x+6y+12

          -12 = 2x + 4y 

          -x/2 - 3 = y     

x^2 + (-x/2 -3)^2 + 2x + 2(-x/2-3) = 0

x^2 + x^2/4 +3x +9 +2x -x - 6 = 0

 4x^2 + x^2 + 12x + 36 + 8x - 4x - 24 = 0

  5x^2 +16x + 12 = 0  

    x = -2  x = -1.2

-x/2 - 3 = y   | x = -2, y = -2    |x = -1.2, y = -2.4

Solution:  Pt(-2,-2) and Pt(-1.2,-2.4)













  

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