General quadratic equations and degenerate loci

Strengthen conic classification beyond memorized coefficient signs. Use factoring, completing the square and real-number constraints to distinguish circles, ellipses, parabolas and hyperbolas from intersecting or parallel lines, a repeated line, a point and an empty real locus. Single-select and multiselect questions develop careful reasoning about the quadratic discriminant and changing parameters. Worked explanations show why a plausible conic label may fail when degeneracy or real existence is not checked.