For a general 2nd-degree equation Ax² + Bxy + Cy² + Dx + Ey + F = 0, the curve is a PARABOLA when:
A$B^2 - 4AC < 0$ (an ellipse case)
B$B^2 - 4AC > 0$ (a hyperbola case)
C$B^2 - 4AC = 0$ (a parabola case)
D$A = B = C$ (no clear classification)
Answer & Solution
Correct answer: C. $B^2 - 4AC = 0$ (a parabola case)
Discriminant Δ = B² − 4AC. Δ = 0 → parabola. Δ < 0 → ellipse (circle if A = C, B = 0). Δ > 0 → hyperbola. Degenerate cases give lines or points.
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