Complete the square for general quadratic conic equations; identify and graph circles, ellipses, parabolas, or hyperbolas.
Write a standard-form conic equation from graph features
Problem
Write the standard-form equation of the circle with center \((2,~-1)\) and radius \(5\). Use the diagram to check the translation signs and radius squared.
Translate the graph features into the circle template one role at a time. Put each center coordinate into a shifted binomial, remembering that the written sign is opposite the coordinate, and put the square of the radius on the other side. A plotted endpoint one radius from the center provides a quick substitution check on both the signs and the scale.
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