Derive the equation of a circle from center/radius and complete the square to identify center/radius.
Read separate center and radius fields from circle standard form
Problem
What are the center and radius of the circle \((x-3)^{2}~+~(y+2)^{2}~=~16\)?
Big Picture
What this problem is really about
Reading circle form requires undoing two different encodings: subtraction hides each center coordinate, while the right side stores the radius squared. We’ll match both binomials to the standard pattern, rewrite addition as subtraction of a negative when needed, and take the nonnegative square root for the radius.
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