by 
Anonymous
ANSWERS: 1
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4x^2 + 4y^2 - 16x - 24y + 43 = 0 Divide by 4: x^2 + y^2 - 4x - 6y + 43/4 = 0 Rearrange: x^2 - 4x + y^2 - 6y + 43/4 = 0 Complete the square for the x terms by adding 4 to both sides: x^2 - 4x + 4 + y^2 - 6y + 43/4 = 4 (x-2)^2 + y^2 - 6y + 43/4 = 4 Complete the square for y terms by adding 9 to both sides: (x-2)^2 + y^2 - 6y + 9 + 43/4 = 4 + 9 (x-2)^2 + (y-3)^2 + 43/4 = 4 + 9 Rearrange: (x-2)^2 + (y-3)^2 = 4 + 9 - 43/4 (x-2)^2 + (y-3)^2 = 13 - 10.75 = 2.25 Note that 2.25 = (1.5)^2 So now you have: (x-2)^2 + (y-3)^2 = (1.5)^2 This is the standard form with the center at (2,3) and a radius of 1.5 Now you do the rest of the problems yourself!
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