Derive the equation of a circle from center/radius and complete the square to identify center/radius.
Classify a point as on, inside, or outside a circle
Problem
Classify point \((3,4)\) as inside, on, or outside the circle \(x^2+y^2=25\).
Big Picture
What this problem is really about
Point position can be decided without taking a square root. We’ll compute the point’s squared distance from the center, compare it with the circle’s radius squared, and interpret a smaller value as interior, equality as boundary, and a larger value as exterior.
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