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Math Help - Why do we write the equation of a circle solved for r^2 and not r?

  1. #1
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    Why do we write the equation of a circle solved for r^2 and not r?

    Do we normally avoid writing the equation of a circle as solved for r to avoid the ambiguity of whether r must be positive? Could we think of r being negative if we describe it as a vector?
    Starting with:
    (x-h)^2+(y-k)^2=r^2
    Solving directly for r would force one to decide whether to put only the principal square root if they require r to be positive:
    r=\sqrt{(x-h)^2+(y-k)^2}
    but if it can be a vector then one could put +/- correct?
    r=\pm\sqrt{(x-h)^2+(y-k)^2}
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    Re: Why do we write the equation of a circle solved for r^2 and not r?

    The reason it's written in terms of \displaystyle r^2 because the equation of a circle follows from Pythagoras' Theorem.
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    Re: Why do we write the equation of a circle solved for r^2 and not r?

    Not to mention that silly symbol, \pm, is wonderfully ambiguous.
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