Derive the equation of a circle from center/radius and complete the square to identify center/radius.
Compare two circles by records and spatial position
Problem
How are the circles \(x^{2}+y^{2}=25\) and \((x-3)^{2}+y^{2}=4\) positioned relative to each other?
Big Picture
What this problem is really about
Two circles’ radii alone do not determine how their boundaries meet; the distance between centers completes the comparison. We’ll read both circle records, compute that distance, compare it with the radius sum and absolute difference, interpret the matching spatial condition, and verify it with a shared boundary location.
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