Assess students' ability to analyze and classify conic sections given a general second-degree equation Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0; tasks include using the discriminant (B^2−4AC) to determine conic type, performing rotation of axes to remove the xy-term, applying quadratic-form and matrix methods or completing the square to obtain standard forms, and extracting centers, axes, vertices, and key geometric parameters.