Assess students' ability to represent general second-degree plane curves as quadratic forms (Ax^2+Bxy+Cy^2+Dx+Ey+F), construct the associated symmetric matrix, compute eigenvalues/eigenvectors to determine and perform orthogonal rotations, translate to the center, obtain canonical forms, classify the conic (ellipse, hyperbola, parabola, degenerate), and extract key geometric parameters (axes, directions, eccentricity) from the diagonalized form.