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

1. ## 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 $\displaystyle r$ to avoid the ambiguity of whether $\displaystyle r$ must be positive? Could we think of $\displaystyle r$ being negative if we describe it as a vector?
Starting with:
$\displaystyle (x-h)^2+(y-k)^2=r^2$
Solving directly for $\displaystyle r$ would force one to decide whether to put only the principal square root if they require r to be positive:
$\displaystyle r=\sqrt{(x-h)^2+(y-k)^2}$
but if it can be a vector then one could put +/- correct?
$\displaystyle r=\pm\sqrt{(x-h)^2+(y-k)^2}$

2. ## 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 $\displaystyle \displaystyle r^2$ because the equation of a circle follows from Pythagoras' Theorem.

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

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