Discriminant - Discriminant of A Conic Section

Discriminant of A Conic Section

For a conic section defined in plane geometry by the real polynomial

the discriminant is equal to

and determines the shape of the conic section. If the discriminant is less than 0, the equation is of an ellipse or a circle. If the discriminant equals 0, the equation is that of a parabola. If the discriminant is greater than 0, the equation is that of a hyperbola. This formula will not work for degenerate cases (when the polynomial factors).

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