Generalization

Here is a general second degree equation in x and y that is used to determine the shape of the outcome graph: Ax² + Bxy + Cy² + Dx + Ey + F = 0.

If B = 0, then the conic section can be determined by the relationship between A and C.

Conic Section - Value of A and C

Parabola - AC = 0, A ¹ C

Circle - A = C

Ellipse - AC > 0, A ¹ C

Hyperbola - AC < 0

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