Complete the square for general quadratic conic equations; identify and graph circles, ellipses, parabolas, or hyperbolas.
Classify a conic and fill only its defined measurements
Problem
Classify \((x~-~3)^2~+~(y~+~2)^2~=~49\) and report only the measurements defined for that conic: its center, size parameter, and any preferred-axis information.
Big Picture
What this problem is really about
Classify the conic from the signs and relative coefficients of its squared terms before naming any measurements. Then use only the parameter vocabulary that belongs to that conic: a center and radial size for a circle, semiaxes for an ellipse or hyperbola, or a vertex and focal distance for a parabola. Symmetry determines whether any axis is genuinely preferred.
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