Derive the equation of a circle from center/radius and complete the square to identify center/radius.
Write the equation of a circle from its center and radius
Problem
Write the center-radius equation of the circle with center \((0,~0)\) and radius \(5\). Show how the center shifts enter the squared terms and how the radius determines the right side.
Big Picture
What this problem is really about
Circle standard form records squared horizontal and vertical distances from the center. We’ll place each center coordinate inside its matching subtraction, simplify any zero shifts, square the radius on the right side, and interpret the equation as the set of points a fixed distance from the center.
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