For a general 2nd-degree equation Ax² + Bxy + Cy² + Dx + Ey + F = 0, t…

Question

For a general 2nd-degree equation Ax² + Bxy + Cy² + Dx + Ey + F = 0, the curve is a PARABOLA when:

Accepted 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.

Answer

$B^2 - 4AC < 0$ (an ellipse case)

Answer

$B^2 - 4AC > 0$ (a hyperbola case)

Answer

$A = B = C$ (no clear classification)