Question: Prove that, except for degenerate cases, the equation Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0 (a) Define

Prove that, except for degenerate cases, the equation 

Ax2 + Bxy + Cy2 + Dx + Ey + F = 0

(a) Define a parabola if B2 – 4AC = 0.

(b) Defines an ellipse (or a circle) if B2 – 4AC < 0.

(c) Defines a hyperbola if B2 – 4AC > 0.

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