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Math Help - origin of a circle

  1. #1
    Junior Member
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    Unhappy origin of a circle

    Center of which circle is closer to the origin?

    x2 + y2 + 6x + 6y = 21
    x2 + y2 + 8x + 8y = 31
    x2 + y2 12x 12y = 43
    x2 + y2 2x 2y = 54
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  2. #2
    Eater of Worlds
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    One thing you could do that would be good practice is to complete the square on each and see.

    Take the first one:

    x^{2}+6x+y^{2}+6y=21

    x^{2}+6x+9+y^{2}+6y+9=39

    (x+3)^{2}+(y+3)^{2}=39

    This one has center at (-3,-3), Check the others.

    But, by inspection, they're all pefect squares. Look at the coefficients of x and y. Which is the smallest?.
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