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Identifying Conics

This guide helps determine the type of conic section represented by the general equation Ax² + Bxy + Cy² + Dx + Ey + F = 0. By examining the coefficients of the terms, we can identify whether the conic is a parabola, hyperbola, ellipse, or circle. Key questions to consider include: Are both x and y squared? Are the coefficients of x² and y² positive? Do x² and y² have the same coefficient? Understanding these relationships will aid in the classification of conics accurately.

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Identifying Conics

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  1. Ax² + Bxy + Cy² +Dx + Ey + F = 0 Identifying Conics

  2. Ax² + Bxy + Cy² +Dx + Ey + F = 0 Identifying Conics Are x and y both squared? yes no Parabola Are x² and y² both positive? no Hyperbola yes Do x² and y² have the same coefficient? no Ellipse Circle yes

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