Complete the square for general quadratic conic equations; identify and graph circles, ellipses, parabolas, or hyperbolas.
Complete squares and report every circle parameter
Problem
Complete the square for \(x^2~+~y^2~-~4x~+~6y~=~12\). Give the circle's standard form, center, and positive radius.
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What this problem is really about
Group the terms by variable and complete each square using the square of half its linear coefficient. Every amount added to form a perfect square must also be added to the other side, preserving an equivalent equation. Once standard form appears, read center coordinates with signs opposite the binomials and take the nonnegative square root of the radius-squared value.
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